메뉴 건너뛰기




Volumn 60, Issue 7, 2007, Pages 1027-1055

On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition

Author keywords

[No Author keywords available]

Indexed keywords


EID: 34249707401     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20187     Document Type: Article
Times cited : (263)

References (53)
  • 1
    • 0001419340 scopus 로고    scopus 로고
    • Effective boundary conditions for laminar flows over periodic rough boundaries
    • Achdou, Y.; Pironneau, O.; Valentin, F. Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys. 147 (1998), no. 1, 187-218.
    • (1998) J. Comput. Phys , vol.147 , Issue.1 , pp. 187-218
    • Achdou, Y.1    Pironneau, O.2    Valentin, F.3
  • 2
    • 34249732298 scopus 로고
    • The existence and asymptotic representation of weak solutions of the flow problem with the condition of regular slippage along rigid walls
    • Alekseenko, S. N. The existence and asymptotic representation of weak solutions of the flow problem with the condition of regular slippage along rigid walls. Sibirsk. Mat. Zh. 35 (1994), no. 2, 235-257;
    • (1994) Sibirsk. Mat. Zh , vol.35 , Issue.2 , pp. 235-257
    • Alekseenko, S.N.1
  • 3
    • 0006415541 scopus 로고
    • Siberian Math. J. 35 (1994), no. 2, 209-230.
    • (1994) Math. J , vol.35 , Issue.2 , pp. 209-230
    • Siberian1
  • 4
    • 0035590150 scopus 로고    scopus 로고
    • Finite element discretization of the Navier-Stokes equations with a free capillary surface
    • Bansen, E. Finite element discretization of the Navier-Stokes equations with a free capillary surface. Numer. Math. 88 (2001), no. 2, 203-235.
    • (2001) Numer. Math , vol.88 , Issue.2 , pp. 203-235
    • Bansen, E.1
  • 5
    • 78149488189 scopus 로고
    • Boundary conditions at a naturally permeable wall
    • Beavers, G. S.; Joseph, D. D. Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30(1967), 197-207.
    • (1967) J. Fluid Mech , vol.30 , pp. 197-207
    • Beavers, G.S.1    Joseph, D.D.2
  • 6
    • 15544361893 scopus 로고    scopus 로고
    • On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions
    • Beirão da Veiga, H. On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions. Comm. Pure Appl. Math. 58 (2005), no. 4, 552-577.
    • (2005) Comm. Pure Appl. Math , vol.58 , Issue.4 , pp. 552-577
    • Beirão da Veiga, H.1
  • 7
    • 0001751765 scopus 로고
    • Remarks on the Euler equation
    • Bourguignon, J. P.; Brezis, H. Remarks on the Euler equation. J. Funct. Anal. 15 (1974), 341-363.
    • (1974) J. Funct. Anal , vol.15 , pp. 341-363
    • Bourguignon, J.P.1    Brezis, H.2
  • 8
    • 0242276990 scopus 로고    scopus 로고
    • The second grade fluid and averaged Euler equations with Navier-slip boundary conditions
    • Busuioc, A. V.; Ratiu, T. S. The second grade fluid and averaged Euler equations with Navier-slip boundary conditions. Nonlinearity 16 (2003), no. 3, 1119-1149.
    • (2003) Nonlinearity , vol.16 , Issue.3 , pp. 1119-1149
    • Busuioc, A.V.1    Ratiu, T.S.2
  • 9
    • 0036341189 scopus 로고    scopus 로고
    • Vector calculus and the topology of domains in 3-space
    • Cantarella, J.; DeTurck, D.; Gluck, H. Vector calculus and the topology of domains in 3-space. Amer. Math. Monthly 109 (2002), no. 5, 409-442.
    • (2002) Amer. Math. Monthly , vol.109 , Issue.5 , pp. 409-442
    • Cantarella, J.1    DeTurck, D.2    Gluck, H.3
  • 10
    • 0030192855 scopus 로고    scopus 로고
    • Homogenization of the Stokes problem with non-homogeneous slip boundary conditions
    • Cioranescu, D.; Donato, P.; Ene, H. I. Homogenization of the Stokes problem with non-homogeneous slip boundary conditions. Mart. Methods Appl. Sci. 19(1996), no. 11, 857-881.
    • (1996) Mart. Methods Appl. Sci , vol.19 , Issue.11 , pp. 857-881
    • Cioranescu, D.1    Donato, P.2    Ene, H.I.3
  • 11
    • 0346997444 scopus 로고    scopus 로고
    • On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary condition
    • Clopeau, T.; Mikelić, A.; Robert, R. On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary condition. Nonlinearity 11 (1998), 1625-1636.
    • (1998) Nonlinearity , vol.11 , pp. 1625-1636
    • Clopeau, T.1    Mikelić, A.2    Robert, R.3
  • 12
    • 0000389320 scopus 로고
    • The Stokes and Navier-Stokes equations with boundary conditions involving the pressure
    • Conca, C.; Murat, F.; Pironneau, O. The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Japan. J. Math. (N.S.) 20 (1994), no. 2, 279-318.
    • (1994) Japan. J. Math. (N.S.) , vol.20 , Issue.2 , pp. 279-318
    • Conca, C.1    Murat, F.2    Pironneau, O.3
  • 14
    • 0000514910 scopus 로고
    • Inviscid limit for vortex patches
    • Constantin, P.; Wu, J. Inviscid limit for vortex patches. Nonlinearity 8 (1995), no. 5,735-742.
    • (1995) Nonlinearity , vol.8 , Issue.5 , pp. 735-742
    • Constantin, P.1    Wu, J.2
  • 15
    • 0001052255 scopus 로고
    • Groups of diffeomorphisms and the notion of an incompressible fluid
    • Ebin, D. G.; Marsden, J. Groups of diffeomorphisms and the notion of an incompressible fluid. Ann. of Math. (2) 92 (1970), 102-163.
    • (1970) Ann. of Math. (2) , vol.92 , pp. 102-163
    • Ebin, D.G.1    Marsden, J.2
  • 16
    • 0036894304 scopus 로고    scopus 로고
    • A coherent analysis of Stokes flows under boundary conditions of friction type. Scientific and engineering computations for the 21st century - methodologies and applications (Shizuoka, 2001)
    • Fujita, H. A coherent analysis of Stokes flows under boundary conditions of friction type. Scientific and engineering computations for the 21st century - methodologies and applications (Shizuoka, 2001). J. Comput. Appl. Math. 149 (2002), no. 1, 57-69.
    • (2002) J. Comput. Appl. Math , vol.149 , Issue.1 , pp. 57-69
    • Fujita, H.1
  • 17
    • 34249651003 scopus 로고    scopus 로고
    • Galdi, G. P. An introduction to the mathematical theory of the Navier-Stokes equations. I. Linearized steady problems. Springer Tracts in Natural Philosophy, 38. Springer, New York, 1994.
    • Galdi, G. P. An introduction to the mathematical theory of the Navier-Stokes equations. Vol. I. Linearized steady problems. Springer Tracts in Natural Philosophy, 38. Springer, New York, 1994.
  • 18
    • 0034403753 scopus 로고    scopus 로고
    • Approximation of the larger eddies in fluid motions. II. A model for space-filtered flow
    • Galdi, G.; Layton, W. J. Approximation of the larger eddies in fluid motions. II. A model for space-filtered flow. Math. Models Methods Appl. Sci. 10 (2000), no. 3, 343-350.
    • (2000) Math. Models Methods Appl. Sci , vol.10 , Issue.3 , pp. 343-350
    • Galdi, G.1    Layton, W.J.2
  • 19
    • 7244253973 scopus 로고    scopus 로고
    • The initial value problem for the Navier-Stokes equations with general slip boundary condition in Holder spaces
    • Itoh, S.; Tanaka, N.; Tani, A. The initial value problem for the Navier-Stokes equations with general slip boundary condition in Holder spaces. J. Math. Fluid Mech. 5 (2003), no. 3, 275-301.
    • (2003) J. Math. Fluid Mech , vol.5 , Issue.3 , pp. 275-301
    • Itoh, S.1    Tanaka, N.2    Tani, A.3
  • 20
    • 0043238030 scopus 로고    scopus 로고
    • On the interface boundary condition of Beavers, Joseph, and Saffman
    • Jäger, W.; Mikelić, A. On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60 (2000), no. 4, 1111-1127.
    • (2000) SIAM J. Appl. Math , vol.60 , Issue.4 , pp. 1111-1127
    • Jäger, W.1    Mikelić, A.2
  • 21
    • 0013203348 scopus 로고    scopus 로고
    • On the roughness-induced effective boundary conditions for an incompressible viscous flow
    • Jäger, W.; Mikelić, A. On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differential Equations 170 (2001), no. 1, 96-122.
    • (2001) J. Differential Equations , vol.170 , Issue.1 , pp. 96-122
    • Jäger, W.1    Mikelić, A.2
  • 22
    • 0037107545 scopus 로고    scopus 로고
    • Slip with friction and penetration with resistance boundary conditions for the Navier-Stokes equations-numerical tests and aspects of the implementation
    • John, V. Slip with friction and penetration with resistance boundary conditions for the Navier-Stokes equations-numerical tests and aspects of the implementation. J. Comput. Appl. Math. 147 (2002), no. 2, 287-300.
    • (2002) J. Comput. Appl. Math , vol.147 , Issue.2 , pp. 287-300
    • John, V.1
  • 24
    • 0040652193 scopus 로고
    • Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary
    • Mathematical Sciences Research Institute Publications, 2. Springer, New York
    • Kato, T. Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary. Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983), 85-98. Mathematical Sciences Research Institute Publications, 2. Springer, New York, 1984.
    • (1984) Seminar on nonlinear partial differential equations (Berkeley, Calif., 1983) , pp. 85-98
    • Kato, T.1
  • 25
    • 0003134154 scopus 로고
    • Nonlinear evolution equations and the Euler flow
    • Kato, T.; Lai, C. Y. Nonlinear evolution equations and the Euler flow. J. Funct. Anal. 56 (1984), no. 1, 15-28.
    • (1984) J. Funct. Anal , vol.56 , Issue.1 , pp. 15-28
    • Kato, T.1    Lai, C.Y.2
  • 26
    • 0005157774 scopus 로고    scopus 로고
    • Discretization of the Navier-Stokes equations with slip boundary condition
    • Liakos, A. Discretization of the Navier-Stokes equations with slip boundary condition. Numer. Methods Partial Differential Equations 17 (2001), no. 1, 26-42.
    • (2001) Numer. Methods Partial Differential Equations , vol.17 , Issue.1 , pp. 26-42
    • Liakos, A.1
  • 28
    • 85020506732 scopus 로고    scopus 로고
    • Lions, P.-L. Mathematical topics in fluid mechanics. 1. Incompressible models. Oxford Lecture Series in Mathematics and Its Applications, 3. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1996.
    • Lions, P.-L. Mathematical topics in fluid mechanics. Vol. 1. Incompressible models. Oxford Lecture Series in Mathematics and Its Applications, 3. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1996.
  • 29
    • 0344233427 scopus 로고    scopus 로고
    • Averaging of the Navier's law on the rapidly oscillating boundary
    • Marušić-Paloka, E. Averaging of the Navier's law on the rapidly oscillating boundary. J. Math. Anal. Appl. 259 (2001), 685-701.
    • (2001) J. Math. Anal. Appl , vol.259 , pp. 685-701
    • Marušić-Paloka, E.1
  • 30
    • 0037359314 scopus 로고    scopus 로고
    • On Navier-Stokes equations with slip boundary conditions in an infinite pipe
    • Mucha, P. B. On Navier-Stokes equations with slip boundary conditions in an infinite pipe. Acta Appl. Math. 76 (2003), no. 1, 1-15.
    • (2003) Acta Appl. Math , vol.76 , Issue.1 , pp. 1-15
    • Mucha, P.B.1
  • 31
    • 0013253496 scopus 로고
    • Sur les lois de l'équilibre et du mouvement des corps élastiques
    • Navier, C. L. M. H. Sur les lois de l'équilibre et du mouvement des corps élastiques. Mem. Acad. R. Sci. Inst. France 6 (1827), 369.
    • (1827) Mem. Acad. R. Sci. Inst. France , vol.6 , pp. 369
    • Navier, C.L.M.H.1
  • 32
    • 0001987016 scopus 로고
    • Über Flüssigkeitsbewegungen bei sehr Kleiner Reibung
    • Teubner, Leipzig
    • Prandtl, L. Über Flüssigkeitsbewegungen bei sehr Kleiner Reibung. Verh. III Int. Math.-Kongr. (Heidelberg 1904), 484-494. Teubner, Leipzig, 1905.
    • (1905) Verh. III Int. Math.-Kongr. (Heidelberg 1904) , pp. 484-494
    • Prandtl, L.1
  • 33
    • 4944228855 scopus 로고    scopus 로고
    • Molecular scale contact line hydrodynamics of immiscible flows
    • Qian, T.; Wang, X. P.; Sheng, P. Molecular scale contact line hydrodynamics of immiscible flows. Phys. Rev. E 68 (2003), 016306.
    • (2003) Phys. Rev. E , vol.68 , pp. 016306
    • Qian, T.1    Wang, X.P.2    Sheng, P.3
  • 34
    • 0015082428 scopus 로고
    • On the boundary condition at the interface of a porous medium
    • Saffman, P. G. On the boundary condition at the interface of a porous medium. Stud. Appl. Wart. 1 (1971), 93-101.
    • (1971) Stud. Appl. Wart , vol.1 , pp. 93-101
    • Saffman, P.G.1
  • 35
    • 0032371860 scopus 로고    scopus 로고
    • Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations
    • Sammartino, M.; Caflisch, R. E. Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. I. Existence for Euler and Prandtl equations. Comm. Math. Phys. 192 (1998), no. 2, 433-461.
    • (1998) Comm. Math. Phys , vol.192 , Issue.2 , pp. 433-461
    • Sammartino, M.1    Caflisch, R.E.2
  • 36
    • 84875267000 scopus 로고    scopus 로고
    • Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II. Construction of the Navier-Stokes solution. Comm. Math. Phys. 192 (1998), no. 2, 463-491.
    • Zero viscosity limit for analytic solutions of the Navier-Stokes equation on a half-space. II. Construction of the Navier-Stokes solution. Comm. Math. Phys. 192 (1998), no. 2, 463-491.
  • 37
    • 0003196889 scopus 로고
    • Hodge decomposition - a method for solving boundary value problems
    • Springer, Berlin
    • Schwarz, G. Hodge decomposition - a method for solving boundary value problems. Lecture Notes in Mathematics, 1607. Springer, Berlin, 1995.
    • (1995) Lecture Notes in Mathematics , vol.1607
    • Schwarz, G.1
  • 39
    • 0001509669 scopus 로고
    • Separating flow near a static contact line: Slip at a wall and shape of a free surface
    • Silliman, W. J.; Scriven, L. E. Separating flow near a static contact line: slip at a wall and shape of a free surface. J. Comput. Phys. 34 (1980), no. 3, 287-313.
    • (1980) J. Comput. Phys , vol.34 , Issue.3 , pp. 287-313
    • Silliman, W.J.1    Scriven, L.E.2
  • 41
    • 0000375589 scopus 로고
    • A certain boundary value problem for the stationary system of Navier-Stokes equations. Boundary value problems of mathematical physics, 8
    • Solonnikov, V. A.; Ščadilov, V. E. A certain boundary value problem for the stationary system of Navier-Stokes equations. Boundary value problems of mathematical physics, 8. Trudy Mat. Inst. Steklov. 125 (1973), 196-210.
    • (1973) Trudy Mat. Inst. Steklov , vol.125 , pp. 196-210
    • Solonnikov, V.A.1    Ščadilov, V.E.2
  • 42
    • 34249733410 scopus 로고    scopus 로고
    • Translation in Proc. Steklov Inst. Math. 125 (1973), 186-199.
    • Translation in Proc. Steklov Inst. Math. 125 (1973), 186-199.
  • 44
    • 85042743964 scopus 로고    scopus 로고
    • On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity
    • Temam, R.; Wang, X. On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997), no. 3-4, 807-828.
    • (1997) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.25 , Issue.3-4 , pp. 807-828
    • Temam, R.1    Wang, X.2
  • 45
    • 0036496598 scopus 로고    scopus 로고
    • Boundary layers associated with incompressible Navier-Stokes equations: The noncharacteristic boundary case
    • Temam, R.; Wang, X. Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. J. Differential Equations 179 (2002), no. 2, 647-686.
    • (2002) J. Differential Equations , vol.179 , Issue.2 , pp. 647-686
    • Temam, R.1    Wang, X.2
  • 46
    • 84988168713 scopus 로고
    • Estimating ∇u by div u and curl u
    • von Wahl, W. Estimating ∇u by div u and curl u. Math. Methods Appl. Sci. 15 (1992), no. 2, 123-143.
    • (1992) Math. Methods Appl. Sci , vol.15 , Issue.2 , pp. 123-143
    • von Wahl, W.1
  • 47
    • 0039841935 scopus 로고    scopus 로고
    • Kato type theorem on zero viscosity limit of Navier-Stokes flows
    • Wang, X. A Kato type theorem on zero viscosity limit of Navier-Stokes flows. Indiana Univ. Math. J. 50 (2001), Special Issue, 223-241.
    • (2001) Indiana Univ. Math. J , vol.50 , Issue.SPEC. ISSUE , pp. 223-241
    • Wang, X.A.1
  • 48
    • 33746314259 scopus 로고    scopus 로고
    • Zero-viscosity limit of the linearized compressible Navier-Stokes equations with highly oscillatory forces in the half-plane
    • Wang, Y.-G.; Xin, Z. Zero-viscosity limit of the linearized compressible Navier-Stokes equations with highly oscillatory forces in the half-plane. SIAM J. Math. Anal. 37 (2005), no. 4, 1256-1298.
    • (2005) SIAM J. Math. Anal , vol.37 , Issue.4 , pp. 1256-1298
    • Wang, Y.-G.1    Xin, Z.2
  • 49
    • 0141782274 scopus 로고    scopus 로고
    • Watanabe, J. On incompressible viscous fluid flows with slip boundary conditions. Proceedings of the 6th Japan-China Joint Seminar on Numerical Mathematics (Tsukuba, 2002). J. Comput. Appl. Math. 159 (2003), no. 1, 161-172.
    • Watanabe, J. On incompressible viscous fluid flows with slip boundary conditions. Proceedings of the 6th Japan-China Joint Seminar on Numerical Mathematics (Tsukuba, 2002). J. Comput. Appl. Math. 159 (2003), no. 1, 161-172.
  • 50
    • 0033480007 scopus 로고    scopus 로고
    • Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane
    • Xin, Z.; Yanagisawa, T. Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane. Comm. Pure Appl. Math. 52 (1999), no. 4, 479-541.
    • (1999) Comm. Pure Appl. Math , vol.52 , Issue.4 , pp. 479-541
    • Xin, Z.1    Yanagisawa, T.2
  • 51
    • 0346401385 scopus 로고    scopus 로고
    • On the global existence of solutions to the Prandtl's system
    • Xin, Z.; Zhang, L. On the global existence of solutions to the Prandtl's system. Adv. Math. 181 (2004), no. 1, 88-133.
    • (2004) Adv. Math , vol.181 , Issue.1 , pp. 88-133
    • Xin, Z.1    Zhang, L.2
  • 52
    • 51249176835 scopus 로고
    • Remarks on spectra of operator rot
    • Yoshida, Z.; Giga, Y. Remarks on spectra of operator rot. Math. Z. 204 (1990), no. 2, 235-245.
    • (1990) Math. Z , vol.204 , Issue.2 , pp. 235-245
    • Yoshida, Z.1    Giga, Y.2
  • 53
    • 0001053022 scopus 로고
    • A two-dimensional non-stationary problem on the flow of an ideal incompressible fluid through a given region
    • Yudovich, V. I. A two-dimensional non-stationary problem on the flow of an ideal incompressible fluid through a given region. Mat. Sb. 4 (1964), no. 64, 562-588.
    • (1964) Mat. Sb , vol.4 , Issue.64 , pp. 562-588
    • Yudovich, V.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.