메뉴 건너뛰기




Volumn 12, Issue 3, 2010, Pages 397-411

Sharp inviscid limit results under navier type boundary conditions. An l p theory

Author keywords

inviscid limit; Navier'Stokes equations; slip boundary conditions

Indexed keywords

FLUX BOUNDARY CONDITIONS; INVISCID LIMIT; SLIP BOUNDARY CONDITIONS; STOKES EQUATIONS;

EID: 77955919768     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-009-0295-4     Document Type: Article
Times cited : (126)

References (41)
  • 1
    • 77950797392 scopus 로고    scopus 로고
    • Regularity for the Navier-Stokes equations with slip boundary condition
    • H.-O. Bae and B. J. Jin, Regularity for the Navier-Stokes equations with slip boundary condition, Proc. Amer. Math. Soc. 136 (2008), 2439-2443.
    • (2008) Proc. Amer. Math. Soc. , vol.136 , pp. 2439-2443
    • Bae, H.-O.1    Jin, B.J.2
  • 2
    • 0001253082 scopus 로고
    • Existence et unicité de la solution de l'équation de Euler en dimension deux
    • C. Bardos, Existence et unicité de la solution de l'équation de Euler en dimension deux, J. Math. Anal. Appl. 40 (1972), 769-790.
    • (1972) J. Math. Anal. Appl. , vol.40 , pp. 769-790
    • Bardos, C.1
  • 3
    • 0009239109 scopus 로고
    • Les équations de Stokes et de Navier- Stokes avec des conditions aux limites sur la pression, in: Collège de France Seminar ' Vol. IX, 169-264
    • C. Bègue, C. Conca, F. Murat and O. Pironneau, Les équations de Stokes et de Navier- Stokes avec des conditions aux limites sur la pression, in: Collège de France Seminar - Vol. IX, 169-264, Pitman Research Notes in Mathematics Series 181, 1988.
    • (1988) Pitman Research Notes in Mathematics Series , vol.181
    • Bègue, C.1    Conca, C.2    Murat, F.3    Pironneau, O.4
  • 4
    • 11144285058 scopus 로고
    • On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid
    • H. Beir̃ao da Veiga, On the solutions in the large of the two-dimensional flow of a nonviscous incompressible fluid, J. Diff. Eq. 54 (1984), 373-389.
    • (1984) J. Diff. Eq. , vol.54 , pp. 373-389
    • Beir̃ao Da Veiga, H.1
  • 5
    • 0000954643 scopus 로고
    • Existence and asymptotic behaviour for strong solutions of the Navier-Stokes equations in the whole space
    • H. Beir̃ao da Veiga, Existence and asymptotic behaviour for strong solutions of the Navier-Stokes equations in the whole space, Indiana University Math. Journal 36 (1987), 149-166.
    • (1987) Indiana University Math Journal , vol.36 , pp. 149-166
    • Beir̃ao Da Veiga, H.1
  • 6
    • 34250085477 scopus 로고
    • Kato's perturbation theory and well-posedness for the Euler equations in bounded domains
    • H. Beir̃ao da Veiga, Kato's perturbation theory and well-posedness for the Euler equations in bounded domains, Archive Rational Mechanics and Analysis 104 (1988), 367-382.
    • (1988) Archive Rational Mechanics and Analysis , vol.104 , pp. 367-382
    • Beir̃ao Da Veiga, H.1
  • 7
    • 45149146994 scopus 로고
    • A well-posedness theorem for non-homogeneous inviscid fluids via a perturbation theorem
    • H. Beir̃ao da Veiga, A well-posedness theorem for non-homogeneous inviscid fluids via a perturbation theorem, J. Diff. Equations 78 (1989), 308-319.
    • (1989) J. Diff. Equations , vol.78 , pp. 308-319
    • Beir̃ao Da Veiga, H.1
  • 8
    • 12144276609 scopus 로고    scopus 로고
    • Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in Rn+
    • H. Beir̃ao da Veiga, Regularity of solutions to a non homogeneous boundary value problem for general Stokes systems in Rn+, Math. Annalen 331 (2005), 203-217.
    • (2005) Math. Annalen , vol.331 , pp. 203-217
    • Beir̃ao Da Veiga, H.1
  • 9
    • 12144261419 scopus 로고    scopus 로고
    • Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip type boundary conditions
    • H. Beir̃ao da Veiga, Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip type boundary conditions, Advances in Differential Equations 9 (2004), no.9-10, 1079-1114.
    • (2004) Advances in Differential Equations , vol.9 , Issue.9-10 , pp. 1079-1114
    • Beir̃ao Da Veiga, H.1
  • 10
    • 77955919256 scopus 로고    scopus 로고
    • Remarks on the Navier-Stokes equations under slip type boundary conditions with linear friction
    • H. Beir̃ao da Veiga, Remarks on the Navier-Stokes equations under slip type boundary conditions with linear friction, Portugaliae Math. 64 (2007), 377-387.
    • (2007) Portugaliae Math. , vol.64 , pp. 377-387
    • Beir̃ao Da Veiga, H.1
  • 11
    • 57749090415 scopus 로고    scopus 로고
    • A review on some contributions to perturbation theory, singular limits and well-posedness
    • H. Beir̃ao da Veiga, A review on some contributions to perturbation theory, singular limits and well-posedness, J. Math. Anal. Appl. 352 (2009), 271-292.
    • (2009) J. Math. Anal. Appl. , vol.352 , pp. 271-292
    • Beir̃ao Da Veiga, H.1
  • 13
    • 0001751765 scopus 로고
    • Remarks on the Euler equation
    • J. P. Bourguignon and H. Brezis, Remarks on the Euler equation, J. Func. Anal. 15 (1974), 341-363.
    • (1974) J. Func. Anal. , vol.15 , pp. 341-363
    • Bourguignon, J.P.1    Brezis, H.2
  • 14
    • 0346997444 scopus 로고    scopus 로고
    • On the vanishing viscosity limit for the 2-D incompressible Navier-Stokes equations with the friction type boundary conditions
    • T. Clopeau, A. Mikelic and R. Robert, On the vanishing viscosity limit for the 2-D incompressible Navier-Stokes equations with the friction type boundary conditions, Non- linearity 11 (1998), 1625-1636.
    • (1998) Non- Linearity , vol.11 , pp. 1625-1636
    • Clopeau, T.1    Mikelic, A.2    Robert, R.3
  • 15
    • 41849149355 scopus 로고    scopus 로고
    • On the Euler equations of incompressible fluids
    • P. Constantin, On the Euler equations of incompressible fluids, Bull. Amer. Math. Soc. 44 (2007), 603-621.
    • (2007) Bull. Amer. Math. Soc. , vol.44 , pp. 603-621
    • Constantin, P.1
  • 17
    • 0001924577 scopus 로고    scopus 로고
    • The inviscid limit for non-smooth vorticity
    • P. Constantin and J. Wu, The inviscid limit for non-smooth vorticity, Indiana Univ. Math. J. 45 (1996), 67-81.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 67-81
    • Constantin, P.1    Wu, J.2
  • 18
    • 0000514910 scopus 로고
    • Inviscid limit for vortex patches
    • P. Constantin and J. Wu, Inviscid limit for vortex patches, Nonlinearity 8 (1995), 735-742.
    • (1995) Nonlinearity , vol.8 , pp. 735-742
    • Constantin, P.1    Wu, J.2
  • 19
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the motion of an incompressible fluid
    • D. G. Ebin and J. E. Marsden, Groups of diffeomorphisms and the motion of an incompressible fluid, Annals of Mathematics 92 (1970), 102-163.
    • (1970) Annals of Mathematics , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.E.2
  • 20
    • 0011913461 scopus 로고    scopus 로고
    • An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Linearized Steady Problems
    • Second corrected printing, Springer-Verlag
    • G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Linearized Steady Problems, Springer Tracts in Natural Philosophy 38, Second corrected printing, Springer-Verlag, 1998.
    • (1998) Springer Tracts in Natural Philosophy , vol.38
    • Galdi, G.P.1
  • 21
    • 0038077120 scopus 로고
    • Curl-conforming finite element methods for Navier-Stokes equations with non-standard bundar onditions in R3
    • Springer Verlag, Berlin-Heidelberg
    • V. Girault, Curl-conforming finite element methods for Navier-Stokes equations with non-standard bundar onditions in R3, Lecture Notes inMathematics 1431, Springer Verlag, Berlin-Heidelberg, 1988.
    • (1988) Lecture Notes in Mathematics , vol.1431
    • Girault, V.1
  • 22
    • 0001751564 scopus 로고
    • Non-stationary flow of an ideal incompressible liquid
    • V. I. Judovich, Non-stationary flow of an ideal incompressible liquid, Zh. Vychisl. Mat. i Mat. Fiz. 3 (1963), 1032-1066.
    • (1963) Zh. Vychisl. Mat. i Mat. Fiz. , vol.3 , pp. 1032-1066
    • Judovich, V.I.1
  • 23
    • 34250521951 scopus 로고
    • On classical solutions of the two-dimensional non-stationary Euler equations
    • T. Kato, On classical solutions of the two-dimensional non-stationary Euler equations, Arch. Rat. Mech. Anal. 25 (1967), 188-200.
    • (1967) Arch. Rat. Mech. Anal. , vol.25 , pp. 188-200
    • Kato, T.1
  • 24
    • 49649144319 scopus 로고
    • Nonstationary flows of viscous and ideal fluids in R3
    • T. Kato, Nonstationary flows of viscous and ideal fluids in R3, J. Functional Anal. 9 (1972), 296-305.
    • (1972) J. Functional Anal. , vol.9 , pp. 296-305
    • Kato, T.1
  • 25
    • 0003123140 scopus 로고
    • Quasi-linear equations of evolution with applications to partial differential equations
    • Springer-Verlag
    • T. Kato, Quasi-linear equations of evolution with applications to partial differential equations, in: Spectral Theory and Differential Equations, Lecture Notes in Mathematics 448, Springer-Verlag, 1975.
    • (1975) Spectral Theory and Differential Equations, Lecture Notes in Mathematics , vol.448
    • Kato, T.1
  • 26
    • 0003134154 scopus 로고
    • Nonlinear evolution equations and the Euler flow
    • T. Kato and C. Y. Lai, Nonlinear evolution equations and the Euler flow, J. Func. Analysis 56 (1984), 15-28.
    • (1984) J. Func. Analysis , vol.56 , pp. 15-28
    • Kato, T.1    Lai, C.Y.2
  • 27
    • 84972559360 scopus 로고
    • On nonsationary flows of viscous and ideal fluids in Lp s(R2)
    • T. Kato and G. Ponce, On nonsationary flows of viscous and ideal fluids in Lp s(R2), Duke Math. J. 55 (1987), 487-499.
    • (1987) Duke Math. J. , Issue.55 , pp. 487-499
    • Kato, T.1    Ponce, G.2
  • 28
    • 84990617895 scopus 로고
    • Commutator estimates and the Euler and Navier-Stokes equations
    • T. Kato and G. Ponce, Commutator estimates and the Euler and Navier-Stokes equations, Comm. Pure Appl. Math. 41 (1988), 891-907.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 891-907
    • Kato, T.1    Ponce, G.2
  • 31
    • 34250514234 scopus 로고
    • Nonstationary plane flows of viscous and ideal fluids
    • F. J. McGrath, Nonstationary plane flows of viscous and ideal fluids, Arch. Rat. Mech. Anal. 27 (1968), 329-348.
    • (1968) Arch. Rat. Mech. Anal. , vol.27 , pp. 329-348
    • McGrath, F.J.1
  • 32
    • 0018305664 scopus 로고
    • The weight function approach to uniqueness of viscous flows in unbounded domains
    • S. Rionero and J. P. Galdi, The weight function approach to uniqueness of viscous flows in unbounded domains, Arch. Rat. Mech. Anal. 69 (1979), 37-52.
    • (1979) Arch. Rat. Mech. Anal. , vol.69 , pp. 37-52
    • Rionero, S.1    Galdi, J.P.2
  • 33
    • 77955925627 scopus 로고
    • Flussi non stazionari di fluidi incompressibili viscosi e ideali in un semipiano
    • P. Secchi, Flussi non stazionari di fluidi incompressibili viscosi e ideali in un semipiano, Ricerche di Matematica 34 (1984), 27-44.
    • (1984) Ricerche di Matematica , vol.34 , pp. 27-44
    • Secchi, P.1
  • 34
    • 0000375589 scopus 로고
    • On a boundary value problem for a stationary system of Navier-Stokes equations
    • V. A. Solonnikov and V. E. Ščadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Proc. Steklov Inst. Math. 125 (1973), 186-199.
    • (1973) Proc. Steklov Inst. Math. , vol.125 , pp. 186-199
    • Solonnikov, V.A.1    Ščadilov, V.E.2
  • 35
    • 0000041315 scopus 로고
    • The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in R3
    • H. S. G. Swann, The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow in R3, Trans. Amer. Math. Soc. 157 (1971), 373-397.
    • (1971) Trans. Amer. Math. Soc. , vol.157 , pp. 373-397
    • Swann, H.S.G.1
  • 36
    • 0039495612 scopus 로고
    • On the Euler equations of incompressible perfect fluids
    • R. Temam, On the Euler equations of incompressible perfect fluids, J. Func. Anal. 20 (1975), 32-43.
    • (1975) J. Func. Anal. , vol.20 , pp. 32-43
    • Temam, R.1
  • 38
    • 0141782274 scopus 로고    scopus 로고
    • On incompressible viscous fluid flows with slip boundary conditions
    • J. Watanabe, On incompressible viscous fluid flows with slip boundary conditions, J. Comp. and Appl. Math. 159 (2003), 161-172.
    • (2003) J. Comp. and Appl. Math. , vol.159 , pp. 161-172
    • Watanabe, J.1
  • 39
    • 84966221742 scopus 로고
    • Existence theorem for the flow of an ideal incompressible fluid in two dimensions
    • A. C. Schaeffer, Existence theorem for the flow of an ideal incompressible fluid in two dimensions, Trans. Amer. Math. Soc. Z. 42 (1937), 497-513.
    • (1937) Trans. Amer. Math. Soc. Z. , vol.42 , pp. 497-513
    • Schaeffer, A.C.1
  • 40
    • 34250940791 scopus 로고
    • Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène incompressible, pendant un temps infiniment longue
    • W. Wolibner, Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène incompressible, pendant un temps infiniment longue, Math. Z. 37 (1933), 698-726.
    • (1933) Math Z. , vol.37 , pp. 698-726
    • Wolibner, W.1
  • 41
    • 34249707401 scopus 로고    scopus 로고
    • On the vanishing viscosity limit for the 3-D Navier-Stokes equations with a slip boundary condition
    • Y. Xiao and Z. Xin, On the vanishing viscosity limit for the 3-D Navier-Stokes equations with a slip boundary condition, Comm. Pure Appl. Math. 60 (2007), no.7, 1027-1055.
    • (2007) Comm. Pure Appl. Math. , vol.60 , Issue.7 , pp. 1027-1055
    • Xiao, Y.1    Xin, Z.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.