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Volumn 38, Issue 1, 2006, Pages 210-232

Navier-Stokes equations with Navier boundary conditions for a bounded domain in the plane

Author keywords

Navier Stokes equations; Vanishing viscosity limit

Indexed keywords

BOUNDED DOMAIN; EULER EQUATIONS; VANISHING VISCOSITY LIMIT;

EID: 33847308713     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/040612336     Document Type: Article
Times cited : (156)

References (28)
  • 2
    • 34250577382 scopus 로고
    • A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations
    • I. BIHARI, A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hungar., 7 (1956), pp. 81-94.
    • (1956) Acta Math. Acad. Sci. Hungar , vol.7 , pp. 81-94
    • BIHARI, I.1
  • 3
    • 0001066894 scopus 로고    scopus 로고
    • A remark on the inviscid limit for two-dimensional incompressible fluids
    • J.-Y. CHEMIN, A remark on the inviscid limit for two-dimensional incompressible fluids, Comm. Partial Differential Equations, 21 (1996), pp. 1771-1779.
    • (1996) Comm. Partial Differential Equations , vol.21 , pp. 1771-1779
    • CHEMIN, J.-Y.1
  • 4
    • 33847266231 scopus 로고    scopus 로고
    • J.-Y. CHEMIN, Perfect Incompressible Fluids, Oxford Lecture Ser. Math. Appl. 14, The Clarendon Press, Oxford University Press, New York, 1998. Translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie.
    • J.-Y. CHEMIN, Perfect Incompressible Fluids, Oxford Lecture Ser. Math. Appl. 14, The Clarendon Press, Oxford University Press, New York, 1998. Translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie.
  • 5
    • 0346997444 scopus 로고    scopus 로고
    • On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
    • T. CLOPEAU, A. MIKELIĆ, AND R. ROBERT, On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions, Nonlinearity, 11 (1998), pp. 1625-1636.
    • (1998) Nonlinearity , vol.11 , pp. 1625-1636
    • CLOPEAU, T.1    MIKELIĆ, A.2    ROBERT, R.3
  • 6
    • 0004227964 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • T. M. FLETT, Differential Analysis, Cambridge University Press, Cambridge, UK, 1980.
    • (1980) Differential Analysis
    • FLETT, T.M.1
  • 7
    • 0002816568 scopus 로고
    • An Introduction to the Mathematical Theory of the Navier-Stokes Equations
    • 38, Springer-Verlag, New York
    • G. P. GALDI, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I, Springer Tracts Nat. Philos. 38, Springer-Verlag, New York, 1994.
    • (1994) Springer Tracts Nat. Philos , vol.1
    • GALDI, G.P.1
  • 10
    • 0013203348 scopus 로고    scopus 로고
    • On the roughness-induced effective boundary conditions for an incompressible viscous flow
    • W. JÄGER AND A. MIKELIĆ, On the roughness-induced effective boundary conditions for an incompressible viscous flow, J. Differential Equations, 170 (2001), pp. 96-122.
    • (2001) J. Differential Equations , vol.170 , pp. 96-122
    • JÄGER, W.1    MIKELIĆ, A.2
  • 11
    • 0037276543 scopus 로고    scopus 로고
    • Couette flows over a rough boundary and drag reduction
    • W. JÄGER AND A. MIKELIC, Couette flows over a rough boundary and drag reduction, Comm. Math. Phys., 232 (2003), pp. 429-455.
    • (2003) Comm. Math. Phys , vol.232 , pp. 429-455
    • JÄGER, W.1    MIKELIC, A.2
  • 12
    • 14644388858 scopus 로고    scopus 로고
    • Derivation and analysis of near wall models for channel and recirculating flows
    • J. VOLKER, W. LAYTON, AND N. SAHIN, Derivation and analysis of near wall models for channel and recirculating flows, Comput. Math. Appl., 48 (2004), pp. 1135-1151.
    • (2004) Comput. Math. Appl , vol.48 , pp. 1135-1151
    • VOLKER, J.1    LAYTON, W.2    SAHIN, N.3
  • 13
    • 0040652193 scopus 로고
    • Seminar on Nonlinear Partial Differential Equations Berkeley, CA, Math. Sci. Res. Inst. Publ. 2, Springer-Verlag, New York
    • T. KATO, Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary, in Seminar on Nonlinear Partial Differential Equations (Berkeley, CA, 1983), Math. Sci. Res. Inst. Publ. 2, Springer-Verlag, New York, 1984, pp. 85-98.
    • (1983) Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary , pp. 85-98
    • KATO, T.1
  • 14
    • 4944266168 scopus 로고    scopus 로고
    • The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity
    • J. P. KELLIHER, The inviscid limit for two-dimensional incompressible fluids with unbounded vorticity, Math. Res. Lett., 11 (2004), pp. 519-528.
    • (2004) Math. Res. Lett , vol.11 , pp. 519-528
    • KELLIHER, J.P.1
  • 16
    • 0003280264 scopus 로고    scopus 로고
    • Mathematical Topics in Fluid Mechanics
    • 3, The Clarendon Press, Oxford University Press, New York
    • P.-L. LIONS, Mathematical Topics in Fluid Mechanics. Vol. 1, Oxford Lecture Ser. Math. Appl. 3, The Clarendon Press, Oxford University Press, New York, 1996.
    • (1996) Oxford Lecture Ser. Math. Appl , vol.1
    • LIONS, P.-L.1
  • 17
    • 22544438444 scopus 로고    scopus 로고
    • On the inviscid limit for two-dimensional incompressible flow with Navier friction condition
    • M. C. LOPES FILHO, H. J. NUSSENZVEIG LOPES, AND G. PLANAS, On the inviscid limit for two-dimensional incompressible flow with Navier friction condition, SIAM J. Math. Anal., 36 (2005), pp. 1130-1141.
    • (2005) SIAM J. Math. Anal , vol.36 , pp. 1130-1141
    • LOPES FILHO, M.C.1    NUSSENZVEIG LOPES, H.J.2    PLANAS, G.3
  • 18
    • 0000911805 scopus 로고
    • On stresses in rarified gases arising from inequalities of temperature
    • J. C. MAXWELL, On stresses in rarified gases arising from inequalities of temperature, Phil. Trans. Royal Society, 1879, pp. 704-712.
    • (1879) Phil. Trans. Royal Society , pp. 704-712
    • MAXWELL, J.C.1
  • 19
    • 0013253496 scopus 로고
    • Sur les lois de l'equilibre et du mouvement des corps élastiques
    • C. M. L. H. NAVIER, Sur les lois de l'equilibre et du mouvement des corps élastiques, Mem. Acad. R. Sci. Inst. France, 6 (1827), p. 369.
    • (1827) Mem. Acad. R. Sci. Inst. France , vol.6 , pp. 369
    • NAVIER, C.M.L.H.1
  • 20
    • 12244278776 scopus 로고
    • Beweis der Existenz einer Lösung der Differentialgleichung dy/dx = f(x,y) ohne Hinzunahme der Cauchy-Lipschitz'schen Bedingung
    • W. F. OSGOOD, Beweis der Existenz einer Lösung der Differentialgleichung dy/dx = f(x,y) ohne Hinzunahme der Cauchy-Lipschitz'schen Bedingung, Monatsch. Math. Phys., 9 (1898), pp. 331-345.
    • (1898) Monatsch. Math. Phys , vol.9 , pp. 331-345
    • OSGOOD, W.F.1
  • 21
    • 33847304496 scopus 로고    scopus 로고
    • A Succinct Proof of Osgood's Lemma, Private communication
    • M. TEHRANCHI, A Succinct Proof of Osgood's Lemma, Private communication.
    • TEHRANCHI, M.1
  • 23
    • 85042743964 scopus 로고    scopus 로고
    • On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
    • R. TEMAM AND X. WANG, On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25 (1997), pp. 807-828.
    • (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.25 , pp. 807-828
    • TEMAM, R.1    WANG, X.2
  • 24
    • 33847296127 scopus 로고    scopus 로고
    • V. I. YUDOVICH, Some bounds for solutions of elliptic equations, Mat. Sb. (N.S.), 59 (1962), pp. 229-244 (in Russian);
    • V. I. YUDOVICH, Some bounds for solutions of elliptic equations, Mat. Sb. (N.S.), 59 (1962), pp. 229-244 (in Russian);
  • 25
    • 33847334732 scopus 로고
    • English translation in
    • English translation in Amer. Math. Soc. Transl. (2), 56 (1966), pp. 1-18.
    • (1966) Amer. Math. Soc. Transl. (2) , vol.56 , pp. 1-18
  • 26
    • 33847261059 scopus 로고    scopus 로고
    • V. I. YUDOVICH, Non-stationary flows of an ideal incompressible fluid, Ž. Vyčisl. Mat. i Mat. Fiz., 3 (1963), pp. 1032-1066 (in Russian).
    • V. I. YUDOVICH, Non-stationary flows of an ideal incompressible fluid, Ž. Vyčisl. Mat. i Mat. Fiz., 3 (1963), pp. 1032-1066 (in Russian).
  • 27
    • 0002131061 scopus 로고
    • Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid
    • V. I. YUDOVICH, Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid, Math. Res. Lett., 2 (1995), pp. 27-38.
    • (1995) Math. Res. Lett , vol.2 , pp. 27-38
    • YUDOVICH, V.I.1
  • 28
    • 0039841935 scopus 로고    scopus 로고
    • A Kato type theorem on zero viscosity limit of Navier-Stokes flows
    • X. WANG, A Kato type theorem on zero viscosity limit of Navier-Stokes flows, Indiana Univ. Math. J., 50 (Special Issue) (2001), pp. 223-241.
    • (2001) Indiana Univ. Math. J , vol.50 , Issue.SPEC. ISSUE , pp. 223-241
    • WANG, X.1


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