메뉴 건너뛰기




Volumn 11, Issue 2, 2009, Pages 233-257

Navier-Stokes equations with shear-thickening viscosity. Regularity up to the boundary

Author keywords

Navier Stokes equations; Regularity up to the boundary; Shear dependent viscosity

Indexed keywords

BASIC IDEA; BOUNDED DOMAIN; EVOLUTION PROBLEM; FIRST ORDER DERIVATIVES; HALF SPACES; NO-SLIP BOUNDARY CONDITIONS; REGULARITY UP TO THE BOUNDARY; SECOND ORDER DERIVATIVES; SHEAR DEPENDENT VISCOSITY; SHEAR THICKENING; STATIONARY PROBLEM; TECHNICAL DIFFICULTIES;

EID: 67949085144     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-008-0257-2     Document Type: Article
Times cited : (32)

References (43)
  • 1
    • 21244502144 scopus 로고    scopus 로고
    • Steady states of anisitropic generalized Newtonian fluids
    • D. APUSHKINSKAYA, M. BILDHAUER and M. FUCHS, Steady states of anisitropic generalized Newtonian fluids, J. Math. Fluid Mech. 7 (2005), 261-297.
    • (2005) J. Math. Fluid Mech , vol.7 , pp. 261-297
    • APUSHKINSKAYA, D.1    BILDHAUER, M.2    FUCHS, M.3
  • 3
    • 12144261419 scopus 로고    scopus 로고
    • H. BEIRÃO DA VEIGA, Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip type boundary conditions, Advances Diff. Eq. 9, no. 9-10, (2004), 1079-1114.
    • H. BEIRÃO DA VEIGA, Regularity for Stokes and generalized Stokes systems under nonhomogeneous slip type boundary conditions, Advances Diff. Eq. 9, no. 9-10, (2004), 1079-1114.
  • 4
    • 15544361893 scopus 로고    scopus 로고
    • On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip and non-slip boundary conditions
    • H. BEIRÃO DA VEIGA, On the regularity of flows with Ladyzhenskaya shear dependent viscosity and slip and non-slip boundary conditions, Comm. Pure Appl. Math. 58 (2005), 552-577.
    • (2005) Comm. Pure Appl. Math , vol.58 , pp. 552-577
    • BEIRÃO DA VEIGA, H.1
  • 5
    • 67949103635 scopus 로고    scopus 로고
    • Navier-Stokes equations with shear thinning viscosity. Regularity up to the boundary
    • in press
    • H. BEIRÃO DA VEIGA, Navier-Stokes equations with shear thinning viscosity. Regularity up to the boundary, J. Math. Fluid. Mech., in press.
    • J. Math. Fluid. Mech
    • BEIRÃO DA VEIGA, H.1
  • 6
    • 85088006427 scopus 로고    scopus 로고
    • On the Ladyzhenskaya- Smagorinsky turbulence model of the NavierStokes equations in smooth domains. The regularity problem
    • in press
    • H. BEIRÃO DA VEIGA, On the Ladyzhenskaya- Smagorinsky turbulence model of the NavierStokes equations in smooth domains. The regularity problem, J. Eur. Math. Soc., in press.
    • J. Eur. Math. Soc
    • BEIRÃO DA VEIGA, H.1
  • 7
    • 67949095535 scopus 로고    scopus 로고
    • 2,l regularity of solutions
    • submitted
    • 2,l regularity of solutions, submitted.
    • BEIRÃO DA VEIGA, H.1
  • 9
    • 4043107362 scopus 로고    scopus 로고
    • Variants of the Stokes problem: The case of anisitropic potentials
    • M. BILDHAUER and M. FUCHS, Variants of the Stokes problem: The case of anisitropic potentials, J. Math. Fluid Mech. 5 (2003), 364-402.
    • (2003) J. Math. Fluid Mech , vol.5 , pp. 364-402
    • BILDHAUER, M.1    FUCHS, M.2
  • 10
    • 0043230255 scopus 로고    scopus 로고
    • Existence for a class of non-Newtonian fluids with energy transfer
    • L. CONSIGLIERI, Existence for a class of non-Newtonian fluids with energy transfer, J. Math. Fluid Mech. 2 (2000), 267-293.
    • (2000) J. Math. Fluid Mech , vol.2 , pp. 267-293
    • CONSIGLIERI, L.1
  • 11
    • 67949097092 scopus 로고    scopus 로고
    • Weak solutions for a class of non-Newtonian fluids with a nonlocal friction boundary condition
    • L. CONSIGLIERI, Weak solutions for a class of non-Newtonian fluids with a nonlocal friction boundary condition, Acta Math. Sinica.
    • Acta Math. Sinica
    • CONSIGLIERI, L.1
  • 12
    • 33845745456 scopus 로고    scopus 로고
    • Steady-state flows of thermal viscous incompressible fluids with convective-radiation effects
    • L. CONSIGLIERI, Steady-state flows of thermal viscous incompressible fluids with convective-radiation effects, Math. Mod. Methods Appl. Sciences 16 (2006), 2013-2027.
    • (2006) Math. Mod. Methods Appl. Sciences , vol.16 , pp. 2013-2027
    • CONSIGLIERI, L.1
  • 13
    • 0037268980 scopus 로고    scopus 로고
    • Vorticity dynamics and turbulence models of Large Eddy Simulations
    • G.-H. COTTET, D. JLROVEANU and B. MICHAUX, Vorticity dynamics and turbulence models of Large Eddy Simulations, M2AN Math. Model. Numer. Anal 37 (2003), 187-207.
    • (2003) M2AN Math. Model. Numer. Anal , vol.37 , pp. 187-207
    • COTTET, G.-H.1    JLROVEANU, D.2    MICHAUX, B.3
  • 14
    • 23944484056 scopus 로고    scopus 로고
    • Strong solutions for generalized Newtonian fluids
    • L. DIENING and M. RŮŽIČKA, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech. 7 (2005), 413-450.
    • (2005) J. Math. Fluid Mech , vol.7 , pp. 413-450
    • DIENING, L.1    RŮŽIČKA, M.2
  • 15
    • 0003369281 scopus 로고    scopus 로고
    • Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids
    • Springer-Verlag, Berlin
    • M. FUCHS and G. SEREGIN, Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids, Lecture Notes in Mathematics 1749, Springer-Verlag, Berlin, 2000.
    • (2000) Lecture Notes in Mathematics , vol.1749
    • FUCHS, M.1    SEREGIN, G.2
  • 16
    • 77956862278 scopus 로고    scopus 로고
    • Mathematical problems in classical and non-Newtonian fluid mechanics
    • G. P. Galdi, A. M. Robertson, R. Rannacher, S. Turek, Birkhäuser-Verlag, Basel
    • G. P. GALDI, Mathematical problems in classical and non-Newtonian fluid mechanics, in: G. P. Galdi, A. M. Robertson, R. Rannacher, S. Turek, Hemodynamical Flows: Modeling, Analysis and Simulation, Oberwolfach Seminars, Birkhäuser-Verlag, Basel, 2007.
    • (2007) Hemodynamical Flows: Modeling, Analysis and Simulation, Oberwolfach Seminars
    • GALDI, G.P.1
  • 18
    • 0035065963 scopus 로고    scopus 로고
    • The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence
    • T. J. R. HUGHES, L. MAZZEI and A. A. OBERAI, The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence, Physics of Fluids 13 (2001), 505-512.
    • (2001) Physics of Fluids , vol.13 , pp. 505-512
    • HUGHES, T.J.R.1    MAZZEI, L.2    OBERAI, A.A.3
  • 19
    • 8844233574 scopus 로고    scopus 로고
    • Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: Comparison of dynamic Smagorinsky and multiscale models over a range of discretizations
    • T. J. R. HUGHES, G. N. WELLS and A. A. WRAY, Energy transfers and spectral eddy viscosity in large-eddy simulations of homogeneous isotropic turbulence: comparison of dynamic Smagorinsky and multiscale models over a range of discretizations, Phys. Fluids 16, no. 11 (2004), 4044-4052.
    • (2004) Phys. Fluids , vol.16 , Issue.11 , pp. 4044-4052
    • HUGHES, T.J.R.1    WELLS, G.N.2    WRAY, A.A.3
  • 20
    • 67949101722 scopus 로고    scopus 로고
    • O. A. LADYZHENSKAYA, On nonlinear problems of continuum mechanics, in: Proc. Int. Congr. Math. (Moscow, 1966), 560-573, Nauka, Moscow, 1968. English transi, in: Amer. Math. Soc. Transi. (2) 70 (1968).
    • O. A. LADYZHENSKAYA, On nonlinear problems of continuum mechanics, in: Proc. Int. Congr. Math. (Moscow, 1966), 560-573, Nauka, Moscow, 1968. English transi, in: Amer. Math. Soc. Transi. (2) 70 (1968).
  • 21
    • 0002859777 scopus 로고
    • Sur de nouvelles équations dans la dynamique des fluides visqueux et leurs résolution globale
    • O. A. LADYHZENSKAYA, Sur de nouvelles équations dans la dynamique des fluides visqueux et leurs résolution globale, Troudi Math. Inst. Steklov CII (1967), 85-104.
    • (1967) Troudi Math. Inst. Steklov , vol.102 , pp. 85-104
    • LADYHZENSKAYA, O.A.1
  • 22
    • 67949124357 scopus 로고    scopus 로고
    • O. A. LADYZHENSKAYA, Sur des modifications des équations de Navier-Stokes pour des grand gradients de vitesses, Séminaire Inst. Steklov 7 (1968), 126-154.
    • O. A. LADYZHENSKAYA, Sur des modifications des équations de Navier-Stokes pour des grand gradients de vitesses, Séminaire Inst. Steklov 7 (1968), 126-154.
  • 24
    • 15544370156 scopus 로고    scopus 로고
    • On regularity of solutions to two-dimensional equations of the dynamics of fluids with nonlinear viscosity
    • O. A. LADYZHENSKAYA and G. A. SEREGIN, On regularity of solutions to two-dimensional equations of the dynamics of fluids with nonlinear viscosity, Zap. Nauch. Sem. Pt. Odel. Mat. Inst. 259 (1999), 145-166.
    • (1999) Zap. Nauch. Sem. Pt. Odel. Mat. Inst , vol.259 , pp. 145-166
    • LADYZHENSKAYA, O.A.1    SEREGIN, G.A.2
  • 26
    • 0001090724 scopus 로고
    • Sur certaines équations paraboliques non-linéaires
    • J.-L. LIONS, Sur certaines équations paraboliques non-linéaires, Bull. Soc. Math. France 93 (1965), 155-175.
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 155-175
    • LIONS, J.-L.1
  • 29
    • 0000365385 scopus 로고    scopus 로고
    • On weak solutions to a class of non-Newtonian incompressilble fluids in bounded three-dimensional domains: The case p > 2
    • J. MÁLEK, J. NEČAS and M. RŮŽIČKA, On weak solutions to a class of non-Newtonian incompressilble fluids in bounded three-dimensional domains: the case p > 2, Advances in Diff. Equations 6 (2001), 257-302.
    • (2001) Advances in Diff. Equations , vol.6 , pp. 257-302
    • MÁLEK, J.1    NEČAS, J.2    RŮŽIČKA, M.3
  • 30
    • 0000034654 scopus 로고
    • Existence and regulaity of solutions and stability of the rest state for fluids with shear dependent viscosity
    • J. MÁLEK, K. R. RAJAGOPAL and M. RŮŽIČKA, Existence and regulaity of solutions and stability of the rest state for fluids with shear dependent viscosity, Math. Models Methods Appl. Sci. 6 (1995), 789-812.
    • (1995) Math. Models Methods Appl. Sci , vol.6 , pp. 789-812
    • MÁLEK, J.1    RAJAGOPAL, K.R.2    RŮŽIČKA, M.3
  • 31
    • 28644446670 scopus 로고    scopus 로고
    • Herschel-Bulkley fluids: Existence and regularity of steady flows
    • J. MÁLEK, M. RŮŽIČKA and V. V. SHELUKHIN, Herschel-Bulkley fluids: Existence and regularity of steady flows, Math. Models Methods Appl. Sci. 15 (2005), 1845-1861.
    • (2005) Math. Models Methods Appl. Sci , vol.15 , pp. 1845-1861
    • MÁLEK, J.1    RŮŽIČKA, M.2    SHELUKHIN, V.V.3
  • 33
    • 0000973918 scopus 로고
    • On elliptic partial differential equations
    • L. NIRENBERG, On elliptic partial differential equations, An. Sc. Norm. Sup. Pisa 13 (1959), 116-162.
    • (1959) An. Sc. Norm. Sup. Pisa , vol.13 , pp. 116-162
    • NIRENBERG, L.1
  • 34
    • 0038538865 scopus 로고
    • Existence, uniqueness and regularity of solutions of the equations of a turbulence model for incompressible fluids
    • C. PARÉS, Existence, uniqueness and regularity of solutions of the equations of a turbulence model for incompressible fluids, Appl. Analysis 43 (1992), 245-296.
    • (1992) Appl. Analysis , vol.43 , pp. 245-296
    • PARÉS, C.1
  • 35
    • 0001634191 scopus 로고
    • Mechanics of Non-Newtonian Fluids
    • G. P. Galdi and J. Nečas eds, Recent Developments in Theoretical Fluid Mechanics, Longman
    • K. R. RAJAGOPAL, Mechanics of Non-Newtonian Fluids, in: G. P. Galdi and J. Nečas (eds.), Recent Developments in Theoretical Fluid Mechanics, 129-162, Research Notes in Mathematics Series 291, Longman, 1993.
    • (1993) Research Notes in Mathematics Series , vol.291 , pp. 129-162
    • RAJAGOPAL, K.R.1
  • 36
    • 18344404502 scopus 로고    scopus 로고
    • A note on steady flow of fluids with shear dependent viscosity
    • M. RŮŽIČKA, A note on steady flow of fluids with shear dependent viscosity, Nonlinear Analysis. TMA 30 (1997), 3029-3039.
    • (1997) Nonlinear Analysis. TMA , vol.30 , pp. 3029-3039
    • RŮŽIČKA, M.1
  • 37
    • 0003196293 scopus 로고    scopus 로고
    • Electrorheological Fluids: Modeling and Mathematical Theory
    • Springer-Verlag, Berlin-Heidelberg
    • M. RŮŽIČKA, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Mathematics 1748, Springer-Verlag, Berlin-Heidelberg, 2000.
    • (2000) Lecture Notes in Mathematics , vol.1748
    • RŮŽIČKA, M.1
  • 38
    • 84867942052 scopus 로고    scopus 로고
    • Modeling, mathematical and numerical analysis of electrorheological fluids
    • M. RŮŽIČKA, Modeling, mathematical and numerical analysis of electrorheological fluids, Applications of Mathematics 49 (2004), 565-609.
    • (2004) Applications of Mathematics , vol.49 , pp. 565-609
    • RŮŽIČKA, M.1
  • 39
    • 0012942618 scopus 로고    scopus 로고
    • Interior regularity for solutions to the modified Navier-Stokes equations
    • G. A. SEREGIN, Interior regularity for solutions to the modified Navier-Stokes equations, J. Math. Fluid Mech. 1 (1999), 235-281.
    • (1999) J. Math. Fluid Mech , vol.1 , pp. 235-281
    • SEREGIN, G.A.1
  • 40
    • 0000286944 scopus 로고
    • Mathematical Principles of Classical Fluid Mechanics
    • Springer-Verlag, Berlin
    • J. SERRIN, Mathematical Principles of Classical Fluid Mechanics, in: Encyclopedia of Physics VIII, 125-263. Springer-Verlag, Berlin, 1959.
    • (1959) Encyclopedia of Physics VIII , pp. 125-263
    • SERRIN, J.1
  • 41
    • 0001957739 scopus 로고
    • General circulation experiments with the primitive equations. I. The basic experiment
    • J. S. SMAGORINSKY, General circulation experiments with the primitive equations. I. The basic experiment, Mon. Weather Rev. 91 (1963), 99-164.
    • (1963) Mon. Weather Rev , vol.91 , pp. 99-164
    • SMAGORINSKY, J.S.1
  • 42
    • 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


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.