메뉴 건너뛰기




Volumn 238, Issue 1-2, 2003, Pages 211-223

Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0037998763     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00220-003-0859-8     Document Type: Article
Times cited : (403)

References (23)
  • 2
    • 84973066506 scopus 로고
    • On the shallow water equations at low Reynolds number
    • Bernardi, C., Pironneau, O.: On the shallow water equations at low Reynolds number. Commun. Partial Diff. Eqs. 16, 59-104 (1991)
    • (1991) Commun. Partial Diff. Eqs. , vol.16 , pp. 59-104
    • Bernardi, C.1    Pironneau, O.2
  • 3
    • 0038212726 scopus 로고    scopus 로고
    • On some compressible fluid models: Korteweg, lubrication and shallow water systems
    • Bresch, D., Desjardins, B., Lin, C.K.: On some compressible fluid models: Korteweg, lubrication and shallow water systems. To appear in Comm. Partial Diff. Eqs. 2002
    • (2002) Comm. Partial Diff. Eqs.
    • Bresch, D.1    Desjardins, B.2    Lin, C.K.3
  • 6
    • 0031495699 scopus 로고    scopus 로고
    • The Cauchy problem and the continuous limit for the multilayer model in geophysical fluid dynamics
    • Colin, T.: The Cauchy problem and the continuous limit for the multilayer model in geophysical fluid dynamics. SIAM J. Math. Anal. 28(3), 516-529 (1997)
    • (1997) SIAM J. Math. Anal. , vol.28 , Issue.3 , pp. 516-529
    • Colin, T.1
  • 7
    • 0000368396 scopus 로고    scopus 로고
    • Rotating fluid at high Rossby number driven by a surface stress: Existence and convergence
    • Colin, T., Fabrie, P.: Rotating fluid at high Rossby number driven by a surface stress: existence and convergence. Adv. Differ. Eqs. 2(5), 715-751 (1997)
    • (1997) Adv. Differ. Eqs. , vol.2 , Issue.5 , pp. 715-751
    • Colin, T.1    Fabrie, P.2
  • 8
    • 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
  • 9
    • 0009049611 scopus 로고    scopus 로고
    • Derivation of the quasigeostrophic potential vorticity equations
    • Desjardins, B., Grenier, E.: Derivation of the quasigeostrophic potential vorticity equations. Adv. Diff. Eqs. 3(5), 715-752 (1998)
    • (1998) Adv. Diff. Eqs. , vol.3 , Issue.5 , pp. 715-752
    • Desjardins, B.1    Grenier, E.2
  • 10
    • 0033542301 scopus 로고    scopus 로고
    • Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions
    • Desjardins, B., Grenier, E., Lions, P.-L., Masmoudi, N.: Incompressible limit for solutions of the isentropic Navier-Stokes equations with Dirichlet boundary conditions. J. Math. Pures Appl. (9) 78(5), 461-471 (1999)
    • (1999) J. Math. Pures Appl. (9) , vol.78 , Issue.5 , pp. 461-471
    • Desjardins, B.1    Grenier, E.2    Lions, P.-L.3    Masmoudi, N.4
  • 11
    • 0040010955 scopus 로고    scopus 로고
    • Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers
    • Embid, P.F., Majda, A.: Low Froude number limiting dynamics for stably stratified flow with small or finite Rossby numbers. Geosphys. Asrtophys. Fluid Dynamics 87, 1-50 (1998)
    • (1998) Geosphys. Asrtophys. Fluid Dynamics , vol.87 , pp. 1-50
    • Embid, P.F.1    Majda, A.2
  • 12
    • 0001755104 scopus 로고    scopus 로고
    • Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity
    • Embid, P.F., Majda, A.: Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity. Comm. Partial Diff. Eqs. 21, 619-658 (1996)
    • (1996) Comm. Partial Diff. Eqs. , vol.21 , pp. 619-658
    • Embid, P.F.1    Majda, A.2
  • 13
    • 0027789426 scopus 로고
    • The energetically consistent shallow water equations
    • Gent, P.: The energetically consistent shallow water equations. J. Atmos. Sci. 50, 1323-1325 (1993)
    • (1993) J. Atmos. Sci. , vol.50 , pp. 1323-1325
    • Gent, P.1
  • 14
    • 0021037838 scopus 로고
    • Balanced models in isentropic coordinates in bounded and periodic domains
    • Gent, P., Williams, J.C.: Balanced models in isentropic coordinates in bounded and periodic domains. Dyn. Atmos. Oceans 7, 67-93 (1983)
    • (1983) Dyn. Atmos. Oceans , vol.7 , pp. 67-93
    • Gent, P.1    Williams, J.C.2
  • 15
    • 0009933535 scopus 로고    scopus 로고
    • Derivation of viscous Saint-Venant system for laminar shallow water; Numerical results
    • Gerbeau, F., Perthame, B.: Derivation of viscous Saint-Venant system for laminar shallow water; Numerical results. Discrete and Continuous Dynamical Systems-series B. 1(1), 89-102 (2001)
    • (2001) Discrete and Continuous Dynamical Systems-series B , vol.1 , Issue.1 , pp. 89-102
    • Gerbeau, F.1    Perthame, B.2
  • 16
    • 0001052077 scopus 로고    scopus 로고
    • Ekman layers of rotating fluids, the case of well prepared initial data
    • Grenier, E., Masmoudi, N.: Ekman layers of rotating fluids, the case of well prepared initial data. Commun. Partial Differential Equations 22(5-6), 953-975 (1997)
    • (1997) Commun. Partial Differential Equations , vol.22 , Issue.5-6 , pp. 953-975
    • Grenier, E.1    Masmoudi, N.2
  • 17
    • 0035511348 scopus 로고    scopus 로고
    • A shallow water model with eddy viscosity for basins with varying bottom topography
    • Levermore, D., Sammartino, M.: A shallow water model with eddy viscosity for basins with varying bottom topography. Nonlinearity 14(6), 1493-1515 (2001)
    • (2001) Nonlinearity , vol.14 , Issue.6 , pp. 1493-1515
    • Levermore, D.1    Sammartino, M.2
  • 18
    • 0002597511 scopus 로고    scopus 로고
    • Mathematical topics in fluid dynamics
    • Oxford: Oxford University Press
    • Lions, P.-L.: Mathematical Topics in Fluid Dynamics. Vol. 2 Compressible Models, Oxford: Oxford University Press, 1998
    • (1998) Compressible Models , vol.2
    • Lions, P.-L.1
  • 19
    • 0034383413 scopus 로고    scopus 로고
    • Ekman layers of rotating fluids: The case of general initial data
    • Masmoudi, N.: Ekman layers of rotating fluids: the case of general initial data. Commun. Pure Appl. Math. 53(4), 432-483 (2000)
    • (2000) Commun. Pure Appl. Math. , vol.53 , Issue.4 , pp. 432-483
    • Masmoudi, N.1
  • 20
    • 16244404505 scopus 로고
    • Un théorème d'existence de solutions d'un problème de shallow water
    • Orenga, P.: Un théorème d'existence de solutions d'un problème de shallow water. Arch. Rat. Mech. Anal. 130(2), 183-204 (1995)
    • (1995) Arch. Rat. Mech. Anal. , vol.130 , Issue.2 , pp. 183-204
    • Orenga, P.1
  • 22
    • 38249033919 scopus 로고
    • Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation
    • Schochet, S.: Singular limits in bounded domains for quasilinear symmetric hyperbolic systems having a vorticity equation. J. Differ. Eqs. 68(3), 400-428 (1987)
    • (1987) J. Differ. Eqs. , vol.68 , Issue.3 , pp. 400-428
    • Schochet, S.1
  • 23
    • 0030586582 scopus 로고    scopus 로고
    • Global existence for the Dirichlet problem for the viscous shallow water equations
    • Sundbye. L.: Global existence for the Dirichlet problem for the viscous shallow water equations. J. Math. Anal. Appl. 202(1), 236-258 (1996)
    • (1996) J. Math. Anal. Appl. , vol.202 , Issue.1 , pp. 236-258
    • Sundbye, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.