메뉴 건너뛰기




Volumn 335, Issue 1, 2015, Pages 93-141

Long Time Dynamics of Forced Critical SQG

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84939891522     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-014-2129-3     Document Type: Article
Times cited : (122)

References (102)
  • 1
    • 84981761614 scopus 로고
    • Lower bounds and uniqueness theorems for solutions of differential equations in a hilbert space
    • Agmon S., Nirenberg L.: Lower bounds and uniqueness theorems for solutions of differential equations in a hilbert space. Comm. Pure Appl. Math. 20, 207–229 (1967)
    • (1967) Comm. Pure Appl. Math , vol.20 , pp. 207-229
    • Agmon, S.1    Nirenberg, L.2
  • 2
    • 4544330532 scopus 로고    scopus 로고
    • Vanishing viscosity limit and long-time behavior for 2d quasi-geostrophic equations
    • Berselli L.C.: Vanishing viscosity limit and long-time behavior for 2d quasi-geostrophic equations. Indiana Univ. Math. J. 51(4), 905–930 (2002)
    • (2002) Indiana Univ. Math. J , vol.51 , Issue.4 , pp. 905-930
    • Berselli, L.C.1
  • 4
    • 4544377751 scopus 로고    scopus 로고
    • A maximum principle applied to quasi-geostrophic equations
    • Córdoba A., Córdoba D.: A maximum principle applied to quasi-geostrophic equations. Comm. Math. Phys. 249(3), 511–528 (2004)
    • (2004) Comm. Math. Phys , vol.249 , Issue.3 , pp. 511-528
    • Córdoba, A.1    Córdoba, D.2
  • 5
    • 79953748556 scopus 로고    scopus 로고
    • Regularity theory for parabolic nonlinear integral operators
    • Caffarelli L., Chan C.H., Vasseur A.: Regularity theory for parabolic nonlinear integral operators. J. Am. Math. Soc. 24(3), 849–869 (2011)
    • (2011) J. Am. Math. Soc , vol.24 , Issue.3 , pp. 849-869
    • Caffarelli, L.1    Chan, C.H.2    Vasseur, A.3
  • 6
    • 0002223508 scopus 로고    scopus 로고
    • On the critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J
    • Dedicated to Professors Ciprian Foias and Roger Temam, Bloomington, IN:
    • Constantin, P., Córdoba, D., Wu, J.: On the critical dissipative quasi-geostrophic equation. Indiana Univ. Math. J. 50 (Special Issue):97–107, 2001. Dedicated to Professors Ciprian Foias and Roger Temam, Bloomington, IN (2000)
    • (2000) 50 (Special Issue):97–107 , vol.2001
    • Constantin, P.1    Córdoba, D.2    Wu, J.3
  • 7
    • 84990581938 scopus 로고
    • Global lyapunov exponents, kaplan–yorke formulas and the dimension of the attractors for 2d navier–stokes equations
    • Constantin P., Foias C.: Global lyapunov exponents, kaplan–yorke formulas and the dimension of the attractors for 2d navier–stokes equations. Comm. Pure Appl. Math. 38(1), 1–27 (1985)
    • (1985) Comm. Pure Appl. Math , vol.38 , Issue.1 , pp. 1-27
    • Constantin, P.1    Foias, C.2
  • 9
    • 0035836678 scopus 로고    scopus 로고
    • Behavior of several two-dimensional fluid equations in singular scenarios
    • Córdoba D., Fefferman C.: Behavior of several two-dimensional fluid equations in singular scenarios. Proc. Natl. Acad. Sci. USA 98(8), 4311–4312 (2001)
    • (2001) Proc. Natl. Acad. Sci. USA , vol.98 , Issue.8 , pp. 4311-4312
    • Córdoba, D.1    Fefferman, C.2
  • 10
    • 0036016138 scopus 로고    scopus 로고
    • Growth of solutions for qg and 2d euler equations
    • Córdoba D., Fefferman C.: Growth of solutions for qg and 2d euler equations. J. Am. Math. Soc. 15(3), 665–670 (2002)
    • (2002) J. Am. Math. Soc , vol.15 , Issue.3 , pp. 665-670
    • Córdoba, D.1    Fefferman, C.2
  • 11
  • 12
    • 0021150102 scopus 로고
    • Determining modes and fractal dimension of turbulent flows
    • Constantin P., Foias C., Manley O.P., Temam R.: Determining modes and fractal dimension of turbulent flows. J. Fluid Mech. 150, 427–440 (1985)
    • (1985) J. Fluid Mech , vol.150 , pp. 427-440
    • Constantin, P.1    Foias, C.2    Manley, O.P.3    Temam, R.4
  • 13
  • 14
    • 0023999086 scopus 로고
    • On the dimension of the attractors in two-dimensional turbulence
    • Constantin P., Foias C., Temam R.: On the dimension of the attractors in two-dimensional turbulence. Phys. D 30(3), 284–296 (1988)
    • (1988) Phys. D , vol.30 , Issue.3 , pp. 284-296
    • Constantin, P.1    Foias, C.2    Temam, R.3
  • 15
    • 84903172604 scopus 로고    scopus 로고
    • Unique ergodicity for fractionally dissipated, stochastically forced 2d Euler equations
    • Constantin P., Glatt-Holtz N., Vicol V.: Unique ergodicity for fractionally dissipated, stochastically forced 2d Euler equations. Comm. Math. Phys. 330(2), 819–857 (2014)
    • (2014) Comm. Math. Phys , vol.330 , Issue.2 , pp. 819-857
    • Constantin, P.1    Glatt-Holtz, N.2    Vicol, V.3
  • 16
    • 54749092935 scopus 로고    scopus 로고
    • The geometric approaches to the possible singularities in the inviscid fluid flows
    • Chae, D.: The geometric approaches to the possible singularities in the inviscid fluid flows. J. Phys. A. 41(36):365501, 11 (2008)
    • (2008) J. Phys. A. 41(36) , pp. 11
    • Chae, D.1
  • 17
    • 0039459032 scopus 로고    scopus 로고
    • Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
    • Cockburn B., Jones D.A., Titi E.S.: Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems. Math. Comp. 66(219), 1073–1087 (1997)
    • (1997) Math. Comp , vol.66 , Issue.219 , pp. 1073-1087
    • Cockburn, B.1    Jones, D.A.2    Titi, E.S.3
  • 18
    • 0037330176 scopus 로고    scopus 로고
    • Global well-posedness in the super-critical dissipative quasi-geostrophic equations
    • Chae D., Lee J.: Global well-posedness in the super-critical dissipative quasi-geostrophic equations. Comm. Math. Phys. 233(2), 297–311 (2003)
    • (2003) Comm. Math. Phys , vol.233 , Issue.2 , pp. 297-311
    • Chae, D.1    Lee, J.2
  • 19
    • 84855663746 scopus 로고    scopus 로고
    • New numerical results for the surface quasi-geostrophic equation
    • Constantin, P., Lai, M.-C., Sharma, R., Tseng, Y.-H., Wu, J.: New numerical results for the surface quasi-geostrophic equation. J. Sci. Comput. 50(1), 1–28 (2012)
    • (2012) J. Sci. Comput , vol.50 , Issue.1 , pp. 1-28
    • Constantin, P.1    Lai, M.-C.2    Sharma, R.3    Tseng, Y.-H.4    Wu, J.5
  • 20
    • 0043172071 scopus 로고
    • Formation of strong fronts in the 2-d quasigeostrophic thermal active scalar
    • Constantin P., Majda A.J., Tabak E.: Formation of strong fronts in the 2-d quasigeostrophic thermal active scalar. Nonlinearity 7(6), 1495–1533 (1994)
    • (1994) Nonlinearity , vol.7 , Issue.6 , pp. 1495-1533
    • Constantin, P.1    Majda, A.J.2    Tabak, E.3
  • 21
    • 33947403194 scopus 로고    scopus 로고
    • A new bernstein’s inequality and the 2d dissipative quasi-geostrophic equation
    • Chen Q., Miao C., Zhang Z.: A new bernstein’s inequality and the 2d dissipative quasi-geostrophic equation. Comm. Math. Phys. 271(3), 821–838 (2007)
    • (2007) Comm. Math. Phys , vol.271 , Issue.3 , pp. 821-838
    • Chen, Q.1    Miao, C.2    Zhang, Z.3
  • 22
    • 0000579087 scopus 로고    scopus 로고
    • Nonsingular surface quasi-geostrophic flow
    • Constantin P., Nie Q., Schörghofer N.: Nonsingular surface quasi-geostrophic flow. Phys. Lett. A 241(3), 168–172 (1998)
    • (1998) Phys. Lett. A , vol.241 , Issue.3 , pp. 168-172
    • Constantin, P.1    Nie, Q.2    Schörghofer, N.3
  • 23
    • 0242330113 scopus 로고
    • ∞ estimates for families of functions with orthonormal derivatives
    • ∞ estimates for families of functions with orthonormal derivatives. Indiana Univ. Math. J. 36(3), 603–616 (1987)
    • (1987) Indiana Univ. Math. J , vol.36 , Issue.3 , pp. 603-616
    • Constantin, P.1
  • 24
    • 0037191442 scopus 로고    scopus 로고
    • Energy spectrum of quasigeostrophic turbulence
    • Constantin P.: Energy spectrum of quasigeostrophic turbulence. Phys. Rev. Lett. 89(18), 184501 (2002)
    • (2002) Phys. Rev. Lett , vol.89 , Issue.18 , pp. 184501
    • Constantin, P.1
  • 26
    • 0032264533 scopus 로고    scopus 로고
    • Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation
    • Córdoba D.: Nonexistence of simple hyperbolic blow-up for the quasi-geostrophic equation. Ann. Math. (2) 148(3), 1135–1152 (1998)
    • (1998) Ann. Math. (2) , vol.148 , Issue.3 , pp. 1135-1152
    • Córdoba, D.1
  • 27
    • 34548348805 scopus 로고    scopus 로고
    • An extension problem related to the fractional Laplacian
    • Caffarelli L., Silvestre L.: An extension problem related to the fractional Laplacian. Comm. Partial Differ. Equ. 32(7–9), 1245–1260 (2007)
    • (2007) Comm. Partial Differ. Equ , vol.32 , Issue.7-9 , pp. 1245-1260
    • Caffarelli, L.1    Silvestre, L.2
  • 28
    • 84897940249 scopus 로고    scopus 로고
    • Absence of anomalous dissipation of energy in forced two dimensional fluid equations
    • Constantin P., Tarfulea A., Vicol V.: Absence of anomalous dissipation of energy in forced two dimensional fluid equations. Arch. Ration. Mech. Anal. 212(3), 875–903 (2014)
    • (2014) Arch. Ration. Mech. Anal , vol.212 , Issue.3 , pp. 875-903
    • Constantin, P.1    Tarfulea, A.2    Vicol, V.3
  • 30
    • 77950869887 scopus 로고    scopus 로고
    • Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
    • Caffarelli L.A., Vasseur A.: Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. Math. (2) 171(3), 1903–1930 (2010)
    • (2010) Ann. Math. (2) , vol.171 , Issue.3 , pp. 1903-1930
    • Caffarelli, L.A.1    Vasseur, A.2
  • 31
    • 79953027828 scopus 로고    scopus 로고
    • The de giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics
    • Caffarelli L.A., Vasseur A.F.: The de giorgi method for regularity of solutions of elliptic equations and its applications to fluid dynamics. Discret. Contin. Dyn. Syst. Ser. S 3(3), 409–427 (2010)
    • (2010) Discret. Contin. Dyn. Syst. Ser. S , vol.3 , Issue.3 , pp. 409-427
    • Caffarelli, L.A.1    Vasseur, A.F.2
  • 32
    • 84868156364 scopus 로고    scopus 로고
    • Nonlinear maximum principles for dissipative linear nonlocal operators and applications
    • Constantin P., Vicol V.: Nonlinear maximum principles for dissipative linear nonlocal operators and applications. Geom. Funct. Anal. 22(5), 1289–1321 (2012)
    • (2012) Geom. Funct. Anal , vol.22 , Issue.5 , pp. 1289-1321
    • Constantin, P.1    Vicol, V.2
  • 33
    • 0033419179 scopus 로고    scopus 로고
    • Behavior of solutions of 2d quasi-geostrophic equations
    • Constantin P., Wu J.: Behavior of solutions of 2d quasi-geostrophic equations. SIAM J. Math. Anal. 30(5), 937–948 (1999)
    • (1999) SIAM J. Math. Anal , vol.30 , Issue.5 , pp. 937-948
    • Constantin, P.1    Wu, J.2
  • 34
    • 54549116855 scopus 로고    scopus 로고
    • Regularity of hölder continuous solutions of the supercritical quasi-geostrophic equation
    • Constantin P., Wu J.: Regularity of hölder continuous solutions of the supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 25(6), 1103–1110 (2008)
    • (2008) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.25 , Issue.6 , pp. 1103-1110
    • Constantin, P.1    Wu, J.2
  • 35
    • 58249085827 scopus 로고    scopus 로고
    • continuity of solutions of supercritical dissipative hydrodynamic transport equations
    • Constantin P., W u. Hölder J.: continuity of solutions of supercritical dissipative hydrodynamic transport equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26(1), 159–180 (2009)
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , Issue.1 , pp. 159-180
    • Constantin, P.1
  • 36
    • 0002069641 scopus 로고
    • Singular integrals and periodic functions
    • Calderón A.P., Zygmund A.: Singular integrals and periodic functions. Studia Math. 14, 249–271 (1954)
    • (1954) Studia Math , vol.14 , pp. 249-271
    • Calderón, A.P.1    Zygmund, A.2
  • 37
    • 79751532095 scopus 로고    scopus 로고
    • Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation
    • Dabkowski M.: Eventual regularity of the solutions to the supercritical dissipative quasi-geostrophic equation. Geom. Funct. Anal. 21(1), 1–13 (2011)
    • (2011) Geom. Funct. Anal , vol.21 , Issue.1 , pp. 1-13
    • Dabkowski, M.1
  • 38
    • 50249090960 scopus 로고    scopus 로고
    • Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space
    • Dong H., Du D.: Global well-posedness and a decay estimate for the critical dissipative quasi-geostrophic equation in the whole space. Discret. Contin. Dyn. Syst. 21(4), 1095–1101 (2008)
    • (2008) Discret. Contin. Dyn. Syst , vol.21 , Issue.4 , pp. 1095-1101
    • Dong, H.1    Du, D.2
  • 39
    • 2442703725 scopus 로고
    • Note on the constantin–foias–temam attractor dimension estimate for two-dimensional turbulence
    • Doering C.R., Gibbon J.D.: Note on the constantin–foias–temam attractor dimension estimate for two-dimensional turbulence. Phys. D 48(2–3), 471–480 (1991)
    • (1991) Phys. D , vol.48 , Issue.2-3 , pp. 471-480
    • Doering, C.R.1    Gibbon, J.D.2
  • 40
    • 70350569716 scopus 로고    scopus 로고
    • Level set dynamics and the non-blowup of the 2d quasi-geostrophic equation
    • Deng J., Hou T.Y., Li R., Yu X.: Level set dynamics and the non-blowup of the 2d quasi-geostrophic equation. Methods Appl. Anal. 13(2), 157–180 (2006)
    • (2006) Methods Appl. Anal , vol.13 , Issue.2 , pp. 157-180
    • Deng, J.1    Hou, T.Y.2    Li, R.3    Yu, X.4
  • 41
    • 84900425142 scopus 로고    scopus 로고
    • Global well-posedness of slightly supercritical active scalar equations
    • Dabkowski M., Kiselev A., Silvestre L., Vicol V.: Global well-posedness of slightly supercritical active scalar equations. Anal. PDE 7(1), 43–72 (2014)
    • (2014) Anal. PDE , vol.7 , Issue.1 , pp. 43-72
    • Dabkowski, M.1    Kiselev, A.2    Silvestre, L.3    Vicol, V.4
  • 42
    • 84862095067 scopus 로고    scopus 로고
    • Global well-posedness for a slightly supercritical surface quasi-geostrophic equation
    • Dabkowski M., Kiselev A., Vicol V.: Global well-posedness for a slightly supercritical surface quasi-geostrophic equation. Nonlinearity 25(5), 1525–1535 (2012)
    • (2012) Nonlinearity , vol.25 , Issue.5 , pp. 1525-1535
    • Dabkowski, M.1    Kiselev, A.2    Vicol, V.3
  • 43
    • 43749097438 scopus 로고    scopus 로고
    • Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations
    • Dong H., Li D.: Spatial analyticity of the solutions to the subcritical dissipative quasi-geostrophic equations. Arch. Ration. Mech. Anal. 189(1), 131–158 (2008)
    • (2008) Arch. Ration. Mech. Anal , vol.189 , Issue.1 , pp. 131-158
    • Dong, H.1    Li, D.2
  • 44
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker’s guide to the fractional sobolev spaces
    • Di Nezza E., Palatucci G., Valdinoci E.: Hitchhiker’s guide to the fractional sobolev spaces. Bull. Sci. Math. 136(5), 521–573 (2012)
    • (2012) Bull. Sci. Math , vol.136 , Issue.5 , pp. 521-573
    • Di Nezza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 45
    • 77950223071 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equations in critical sobolev spaces: smoothing effect and global well-posedness
    • Dong H.: Dissipative quasi-geostrophic equations in critical sobolev spaces: smoothing effect and global well-posedness. Discrete Contin. Dyn. Syst. 26(4), 1197–1211 (2010)
    • (2010) Discrete Contin. Dyn. Syst , vol.26 , Issue.4 , pp. 1197-1211
    • Dong, H.1
  • 46
    • 70349918312 scopus 로고    scopus 로고
    • Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
    • Dong H., Pavlović N.: Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces. Comm. Math. Phys. 290(3), 801–812 (2009)
    • (2009) Comm. Math. Phys , vol.290 , Issue.3 , pp. 801-812
    • Dong, H.1    Pavlović, N.2
  • 47
    • 69749083481 scopus 로고    scopus 로고
    • A regularity criterion for the dissipative quasi-geostrophic equations
    • Dong H., Pavlović N.: A regularity criterion for the dissipative quasi-geostrophic equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 26(5), 1607–1619 (2009)
    • (2009) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.26 , Issue.5 , pp. 1607-1619
    • Dong, H.1    Pavlović, N.2
  • 48
    • 22244442110 scopus 로고
    • Determining nodes for the kuramoto-sivashinsky equation
    • Foias C., Kukavica I.: Determining nodes for the kuramoto-sivashinsky equation. J. Dynam. Differ. Equ. 7(2), 365–373 (1995)
    • (1995) J. Dynam. Differ. Equ , vol.7 , Issue.2 , pp. 365-373
    • Foias, C.1    Kukavica, I.2
  • 50
    • 0000640737 scopus 로고
    • Modelling of the interaction of small and large eddies in two-dimensional turbulent flows
    • Foias C., Manley O., Temam R.: Modelling of the interaction of small and large eddies in two-dimensional turbulent flows. RAIRO Modél. Math. Anal. Numér. 22(1), 93–118 (1988)
    • (1988) RAIRO Modél. Math. Anal. Numér , vol.22 , Issue.1 , pp. 93-118
    • Foias, C.1    Manley, O.2    Temam, R.3
  • 51
    • 0020830393 scopus 로고
    • Asymptotic analysis of the navier–stokes equations
    • Foias C., Manley O.P., Temam R., Trève Y.M.: Asymptotic analysis of the navier–stokes equations. Phys. D 9(1–2), 157–188 (1983)
    • (1983) Phys. D , vol.9 , Issue.1-2 , pp. 157-188
    • Foias, C.1    Manley, O.P.2    Temam, R.3    Trève, Y.M.4
  • 52
    • 0002449201 scopus 로고
    • Sur le comportement global des solutions non-stationnaires des équations de navier–stokes en dimension 2
    • Foias C., Prodi G.: Sur le comportement global des solutions non-stationnaires des équations de navier–stokes en dimension 2. Rend. Sem. Mat. Univ. Padova 39, 1–34 (1967)
    • (1967) Rend. Sem. Mat. Univ. Padova , vol.39 , pp. 1-34
    • Foias, C.1    Prodi, G.2
  • 53
    • 70350580506 scopus 로고    scopus 로고
    • Nonlinear instability for the critically dissipative quasi-geostrophic equation
    • Friedlander S., Pavlović N., Vicol V.: Nonlinear instability for the critically dissipative quasi-geostrophic equation. Comm. Math. Phys. 292(3), 797–810 (2009)
    • (2009) Comm. Math. Phys , vol.292 , Issue.3 , pp. 797-810
    • Friedlander, S.1    Pavlović, N.2    Vicol, V.3
  • 54
    • 79952484503 scopus 로고    scopus 로고
    • Analytic sharp fronts for the surface quasi-geostrophic equation
    • Fefferman C., Rodrigo J.L.: Analytic sharp fronts for the surface quasi-geostrophic equation. Comm. Math. Phys. 303(1), 261–288 (2011)
    • (2011) Comm. Math. Phys , vol.303 , Issue.1 , pp. 261-288
    • Fefferman, C.1    Rodrigo, J.L.2
  • 55
    • 0000076092 scopus 로고
    • Variétés inertielles des équations différentielles dissipatives
    • Foias C., Sell G.R., Temam R.: Variétés inertielles des équations différentielles dissipatives. C. R. Acad. Sci. Paris Sér. I Math. 301(5), 139–141 (1985)
    • (1985) C. R. Acad. Sci. Paris Sér. I Math , vol.301 , Issue.5 , pp. 139-141
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 56
    • 0000640733 scopus 로고
    • Inertial manifolds for nonlinear evolutionary equations
    • Foias C., Sell G.R., Temam R.: Inertial manifolds for nonlinear evolutionary equations. J. Differ. Equ. 73(2), 309–353 (1988)
    • (1988) J. Differ. Equ , vol.73 , Issue.2 , pp. 309-353
    • Foias, C.1    Sell, G.R.2    Temam, R.3
  • 57
    • 84966204481 scopus 로고
    • Determination of the solutions of the navier–stokes equations by a set of nodal values
    • Foias C., Temam R.: Determination of the solutions of the navier–stokes equations by a set of nodal values. Math. Comp. 43(167), 117–133 (1984)
    • (1984) Math. Comp , vol.43 , Issue.167 , pp. 117-133
    • Foias, C.1    Temam, R.2
  • 58
    • 0000166593 scopus 로고
    • Determining nodes, finite difference schemes and inertial manifolds
    • Foias C., Titi E.S.: Determining nodes, finite difference schemes and inertial manifolds. Nonlinearity 4(1), 135–153 (1991)
    • (1991) Nonlinearity , vol.4 , Issue.1 , pp. 135-153
    • Foias, C.1    Titi, E.S.2
  • 59
    • 0013419090 scopus 로고    scopus 로고
    • Attractor dimension and small length scale estimates for the three-dimensional navier–stokes equations
    • Gibbon J.D., Titi E.S.: Attractor dimension and small length scale estimates for the three-dimensional navier–stokes equations. Nonlinearity 10(1), 109–119 (1997)
    • (1997) Nonlinearity , vol.10 , Issue.1 , pp. 109-119
    • Gibbon, J.D.1    Titi, E.S.2
  • 60
    • 0003293929 scopus 로고
    • Asymptotic behavior of dissipative systems
    • American Mathematical Society, Providence, RI:
    • Hale, J.K.: Asymptotic behavior of dissipative systems. Mathematical Surveys and Monographs, vol. 25. American Mathematical Society, Providence, RI (1988)
    • (1988) Mathematical Surveys and Monographs , vol.25
    • Hale, J.K.1
  • 61
    • 34447123394 scopus 로고    scopus 로고
    • Global solutions of the super-critical 2d quasi-geostrophic equation in besov spaces
    • Hmidi T., Keraani S.: Global solutions of the super-critical 2d quasi-geostrophic equation in besov spaces. Adv. Math. 214(2), 618–638 (2007)
    • (2007) Adv. Math , vol.214 , Issue.2 , pp. 618-638
    • Hmidi, T.1    Keraani, S.2
  • 63
    • 38249013027 scopus 로고
    • On the number of determining nodes for the 2d navier–stokes equations
    • Jones D.A., Titi E.S.: On the number of determining nodes for the 2d navier–stokes equations. J. Math. Anal. Appl. 168(1), 72–88 (1992)
    • (1992) J. Math. Anal. Appl , vol.168 , Issue.1 , pp. 72-88
    • Jones, D.A.1    Titi, E.S.2
  • 64
    • 0000646281 scopus 로고
    • Upper bounds on the number of determining modes, nodes, and volume elements for the navier–stokes equations
    • Jones D.A., Titi E.S.: Upper bounds on the number of determining modes, nodes, and volume elements for the navier–stokes equations. Indiana Univ. Math. J. 42(3), 875–887 (1993)
    • (1993) Indiana Univ. Math. J , vol.42 , Issue.3 , pp. 875-887
    • Jones, D.A.1    Titi, E.S.2
  • 65
    • 11144329539 scopus 로고    scopus 로고
    • Existence and uniqueness of the solution to the dissipative 2d quasi-geostrophic equations in the sobolev space
    • Ju N.: Existence and uniqueness of the solution to the dissipative 2d quasi-geostrophic equations in the sobolev space. Comm. Math. Phys. 251(2), 365–376 (2004)
    • (2004) Comm. Math. Phys , vol.251 , Issue.2 , pp. 365-376
    • Ju, N.1
  • 66
    • 21244497902 scopus 로고    scopus 로고
    • The maximum principle and the global attractor for the dissipative 2d quasi-geostrophic equations
    • Ju N.: The maximum principle and the global attractor for the dissipative 2d quasi-geostrophic equations. Comm. Math. Phys. 255(1), 161–181 (2005)
    • (2005) Comm. Math. Phys , vol.255 , Issue.1 , pp. 161-181
    • Ju, N.1
  • 67
    • 34247536873 scopus 로고    scopus 로고
    • Dissipative 2d quasi-geostrophic equation: local well-posedness, global regularity and similarity solutions
    • Ju N.: Dissipative 2d quasi-geostrophic equation: local well-posedness, global regularity and similarity solutions. Indiana Univ. Math. J. 56(1), 187–206 (2007)
    • (2007) Indiana Univ. Math. J , vol.56 , Issue.1 , pp. 187-206
    • Ju, N.1
  • 68
    • 79956367250 scopus 로고    scopus 로고
    • Nonlocal maximum principles for active scalars
    • Kiselev A.: Nonlocal maximum principles for active scalars. Adv. Math. 227(5), 1806–1826 (2011)
    • (2011) Adv. Math , vol.227 , Issue.5 , pp. 1806-1826
    • Kiselev, A.1
  • 70
    • 75149114116 scopus 로고    scopus 로고
    • Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation
    • Kiselev A., Nazarov F.: Global regularity for the critical dispersive dissipative surface quasi-geostrophic equation. Nonlinearity 23(3), 549–554 (2010)
    • (2010) Nonlinearity , vol.23 , Issue.3 , pp. 549-554
    • Kiselev, A.1    Nazarov, F.2
  • 71
    • 33846785446 scopus 로고    scopus 로고
    • Global well-posedness for the critical 2d dissipative quasi-geostrophic equation
    • Kiselev A., Nazarov F., Volberg A.: Global well-posedness for the critical 2d dissipative quasi-geostrophic equation. Invent. Math. 167(3), 445–453 (2007)
    • (2007) Invent. Math , vol.167 , Issue.3 , pp. 445-453
    • Kiselev, A.1    Nazarov, F.2    Volberg, A.3
  • 72
    • 84990617895 scopus 로고
    • Commutator estimates and the euler and Navier–Stokes equations
    • Kato T., Ponce G.: Commutator estimates and the euler and Navier–Stokes equations. Comm. Pure Appl. Math. 41(7), 891–907 (1988)
    • (1988) Comm. Pure Appl. Math , vol.41 , Issue.7 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 73
    • 84968502715 scopus 로고
    • Well-posedness of the initial value problem for the korteweg–de vries equation
    • Kenig C.E., Ponce G., Vega L.: Well-posedness of the initial value problem for the korteweg–de vries equation. J. Am. Math. Soc. 4(2), 323–347 (1991)
    • (1991) J. Am. Math. Soc , vol.4 , Issue.2 , pp. 323-347
    • Kenig, C.E.1    Ponce, G.2    Vega, L.3
  • 74
    • 0001024872 scopus 로고
    • On the number of determining nodes for the ginzburg-landau equation
    • Kukavica I.: On the number of determining nodes for the ginzburg-landau equation. Nonlinearity 5(5), 997–1006 (1992)
    • (1992) Nonlinearity , vol.5 , Issue.5 , pp. 997-1006
    • Kukavica, I.1
  • 75
    • 0030577971 scopus 로고    scopus 로고
    • Level sets of the vorticity and the stream function for the 2d periodic navier–stokes equations with potential forces
    • Kukavica I.: Level sets of the vorticity and the stream function for the 2d periodic navier–stokes equations with potential forces. J. Differ. Equ. 126(2), 374–388 (1996)
    • (1996) J. Differ. Equ , vol.126 , Issue.2 , pp. 374-388
    • Kukavica, I.1
  • 76
    • 77950668101 scopus 로고    scopus 로고
    • Log–log convexity and backward uniqueness
    • Kukavica, I.: Log–log convexity and backward uniqueness. Proc. Am. Math. Soc, 135(8):2415–2421 (2007)
    • (2007) Proc. Am. Math. Soc , vol.135 , Issue.8 , pp. 2415-2421
    • Kukavica, I.1
  • 77
    • 79951849382 scopus 로고    scopus 로고
    • On the analyticity and gevrey-class regularity up to the boundary for the euler equations
    • Kukavica I., Vicol V.: On the analyticity and gevrey-class regularity up to the boundary for the euler equations. Nonlinearity 24(3), 765–796 (2011)
    • (2011) Nonlinearity , vol.24 , Issue.3 , pp. 765-796
    • Kukavica, I.1    Vicol, V.2
  • 79
    • 36448933442 scopus 로고    scopus 로고
    • Existence and regularity of weak solutions to the quasi-geostrophic equations in the spaces L
    • p or $${\dot{h}^{-1/2}}$$h˙-1/2. Comm. Math. Phys. 277(1), 45–67 (2008)
    • (2008) Comm. Math. Phys , vol.277 , Issue.1 , pp. 45-67
    • Marchand, F.1
  • 80
    • 33747198457 scopus 로고    scopus 로고
    • Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space
    • Miura H.: Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space. Comm. Math. Phys. 267(1), 141–157 (2006)
    • (2006) Comm. Math. Phys , vol.267 , Issue.1 , pp. 141-157
    • Miura, H.1
  • 81
    • 78650136818 scopus 로고    scopus 로고
    • Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalized viscosity: a numerical study
    • Ohkitani K., Sakajo T.: Oscillatory damping in long-time evolution of the surface quasi-geostrophic equations with generalized viscosity: a numerical study. Nonlinearity 23(12), 3029–3051 (2010)
    • (2010) Nonlinearity , vol.23 , Issue.12 , pp. 3029-3051
    • Ohkitani, K.1    Sakajo, T.2
  • 82
    • 0030876020 scopus 로고    scopus 로고
    • Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow
    • Ohkitani K., Yamada M.: Inviscid and inviscid-limit behavior of a surface quasigeostrophic flow. Phys. Fluids 9(4), 876–882 (1997)
    • (1997) Phys. Fluids , vol.9 , Issue.4 , pp. 876-882
    • Ohkitani, K.1    Yamada, M.2
  • 87
    • 84966255681 scopus 로고
    • Fourier series in several variables
    • Shapiro V.L.: Fourier series in several variables. Bull. Am. Math. Soc. 70, 48–93 (1964)
    • (1964) Bull. Am. Math. Soc , vol.70 , pp. 48-93
    • Shapiro, V.L.1
  • 88
    • 76849110369 scopus 로고    scopus 로고
    • Eventual regularization for the slightly supercritical quasi-geostrophic equation
    • Silvestre L.: Eventual regularization for the slightly supercritical quasi-geostrophic equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 27(2), 693–704 (2010)
    • (2010) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.27 , Issue.2 , pp. 693-704
    • Silvestre, L.1
  • 90
    • 1642618627 scopus 로고    scopus 로고
    • Asymptotic behavior to dissipative quasi-geostrophic flows
    • Schonbek M.E., Schonbek T.P.: Asymptotic behavior to dissipative quasi-geostrophic flows. SIAM J. Math. Anal. 35(2), 357–375 (2003)
    • (2003) SIAM J. Math. Anal , vol.35 , Issue.2 , pp. 357-375
    • Schonbek, M.E.1    Schonbek, T.P.2
  • 92
    • 84872942460 scopus 로고    scopus 로고
    • On the loss of continuity for super-critical drift-diffusion equations
    • Silvestre L., Vicol V., Zlatoš A.: On the loss of {ccaron;ontinuity for super-critical drift-diffusion equations. Arch. Ration. Mech. Anal. 207(3), 845–877 (2013)
    • (2013) Arch. Ration. Mech. Anal , vol.207 , Issue.3 , pp. 845-877
    • Silvestre, L.1    Vicol, V.2    Zlatoš, A.3
  • 93
    • 0003263410 scopus 로고
    • Introduction to Fourier analysis on Euclidean spaces
    • Princeton University Press, Princeton, NJ:
    • Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton University Press, Princeton, NJ (1971)
    • (1971) Princeton Mathematical Series , vol.32
    • Stein, E.M.1    Weiss, G.2
  • 94
    • 0003203437 scopus 로고
    • Pseudodifferential operators and nonlinear PDE
    • Birkhäuser Boston Inc., Boston, MA:
    • Taylor, M.E.: Pseudodifferential operators and nonlinear PDE. Progress in Mathematics, vol. 100. Birkhäuser Boston Inc., Boston, MA (1991)
    • (1991) Progress in Mathematics , vol.100
    • Taylor, M.E.1
  • 96
    • 0034626637 scopus 로고    scopus 로고
    • Stokes waves in hardy spaces and as distributions
    • Toland J.F.: Stokes waves in hardy spaces and as distributions. J. Math. Pures Appl. 79(9), 901–917 (2000)
    • (2000) J. Math. Pures Appl , vol.79 , Issue.9 , pp. 901-917
    • Toland, J.F.1
  • 97
    • 84875274620 scopus 로고    scopus 로고
    • On dimension of the global attractor for 2d quasi-geostrophic equations
    • Wang M., Tang Y.: On dimension of the global attractor for 2d quasi-geostrophic equations. Nonlinear Anal. Real World Appl. 14(4), 1887–1895 (2013)
    • (2013) Nonlinear Anal. Real World Appl , vol.14 , Issue.4 , pp. 1887-1895
    • Wang, M.1    Tang, Y.2
  • 98
    • 18744399570 scopus 로고    scopus 로고
    • Wu, J.: Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces. SIAM J. Math. Anal. 36(3):1014–1030 (2004/05)
    • Wu, J.: Global solutions of the 2D dissipative quasi-geostrophic equation in Besov spaces. SIAM J. Math. Anal. 36(3):1014–1030 (2004/05)
  • 99
    • 85099638991 scopus 로고    scopus 로고
    • p data. Electron. J. Differ. Equ, 56, 1–13 (2001)
    • p data. Electron. J. Differ. Equ, 56, 1–13 (2001)
  • 100
    • 84860610382 scopus 로고    scopus 로고
    • Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation
    • Xue L., Zheng X.: Note on the well-posedness of a slightly supercritical surface quasi-geostrophic equation. J. Differ. Equ. 253(2), 795–813 (2012)
    • (2012) J. Differ. Equ , vol.253 , Issue.2 , pp. 795-813
    • Xue, L.1    Zheng, X.2
  • 101
    • 35248823548 scopus 로고    scopus 로고
    • Remarks on the global regularity for the super-critical 2d dissipative quasi-geostrophic equation
    • Yu X.: Remarks on the global regularity for the super-critical 2d dissipative quasi-geostrophic equation. J. Math. Anal. Appl. 339(1), 359–371 (2008)
    • (2008) J. Math. Anal. Appl , vol.339 , Issue.1 , pp. 359-371
    • Yu, X.1
  • 102
    • 0002266080 scopus 로고    scopus 로고
    • Optimal bounds on the dimension of the attractor of the Navier–Stokes equations
    • Ziane M.: Optimal bounds on the dimension of the attractor of the Navier–Stokes equations. Phys. D Nonlinear Phenom. 105(1), 1–19 (1997)
    • (1997) Phys. D Nonlinear Phenom , vol.105 , Issue.1 , pp. 1-19
    • Ziane, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.