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Volumn 9, Issue 1, 2010, Pages 1-46

Existence of weak solutions for unsteady motions of generalized Newtonian fluids

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EID: 83455163436     PISSN: 0391173X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (185)

References (52)
  • 1
    • 34250138457 scopus 로고
    • Semicontinuity problems in the calculus of variations
    • E. ACERBI and N. FUSCO, Semicontinuity problems in the calculus of variations, Arch. Ration. Mech. Anal. 86 (1984), 125-145.
    • (1984) Arch. Ration. Mech. Anal. , vol.86 , pp. 125-145
    • Acerbi, E.1    Fusco, N.2
  • 2
    • 21844527161 scopus 로고
    • Stability of the rest state of a viscous incompressible fluid
    • H. AMANN, Stability of the rest state of a viscous incompressible fluid, Arch. Ration. Mech. Anal. 126 (1994), 231-242.
    • (1994) Arch. Ration. Mech. Anal. , vol.126 , pp. 231-242
    • Amann, H.1
  • 5
    • 84957251972 scopus 로고
    • Young measure-valued solutions for non-Newtonian incompressible fluids
    • H. BELLOUT, F. BLOOM and J. NEČAS, Young measure-valued solutions for non-Newtonian incompressible fluids, Comm. Partial Differential Equations 19 (1994), 1763-1803.
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 1763-1803
    • Bellout, H.1    Bloom, F.2    Nečas, J.3
  • 7
    • 41449103407 scopus 로고    scopus 로고
    • p-theory for a class of non-Newtonian fluids
    • p-theory for a class of non-Newtonian fluids, SIAM J. Math. Anal. 39 (2007), 379-421.
    • (2007) SIAM J. Math. Anal. , vol.39 , pp. 379-421
    • Bothe, D.1    Prüss, J.2
  • 8
    • 0008999457 scopus 로고
    • Quelques exemples de fluides newtoniens generalisés
    • Mathematical Topics in Fluid Mechanics Lisbon, (1991) (Harlow)Longman Sci. Tech., Harlow
    • D. CIORANESCU, Quelques exemples de fluides newtoniens generalisés, In: "Mathematical Topics in Fluid Mechanics" (Lisbon, 1991) (Harlow), Pitman Res. Notes Math. Ser., Vol. 274, Longman Sci. Tech., Harlow, 1992, 1-31.
    • (1992) Pitman Res. Notes Math. Ser. , vol.274 , pp. 1-31
    • Cioranescu, D.1
  • 9
    • 84966261604 scopus 로고
    • Extensions of Hardy spaces and their use in analysis
    • R. R. COIFMAN and G. WEISS, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
    • (1977) Bull. Amer. Math. Soc. , vol.83 , pp. 569-645
    • Coifman, R.R.1    Weiss, G.2
  • 10
    • 15544361893 scopus 로고    scopus 로고
    • On the regularity of flows with ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions
    • DOI 10.1002/cpa.20036
    • H. BEIRÃO DA VEIGA, On the regularity of flows with Ladyzhenskaya shear-dependent viscosity and slip or nonslip boundary conditions, Comm. Pure Appl. Math. 58 (2005), 552-577. (Pubitemid 40406005)
    • (2005) Communications on Pure and Applied Mathematics , vol.58 , Issue.4 , pp. 552-577
    • Beirao Da Veiga, H.1
  • 12
    • 0002250134 scopus 로고
    • Springer-Verlag, Berlin, with appendices by Antonio Córdoba, and Robert Fefferman, and two by Roberto Moriyón, Lecture Notes in Mathematics
    • n", Springer-Verlag, Berlin, 1975, with appendices by Antonio Córdoba, and Robert Fefferman, and two by Roberto Moriyón, Lecture Notes in Mathematics, Vol. 481.
    • (1975) n , vol.481
    • De Guzmán, M.1
  • 13
    • 41549098727 scopus 로고    scopus 로고
    • On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications
    • DOI 10.1051/cocv:2007049
    • L. DIENING, J. MÁLEK and M. STEINHAUER, On Lipschitz truncations of Sobolev functions (with variable exponent) and their selected applications, ESAIM Control Optim. Calc. Var. 14 (2008), 211-232, DOI: 10.1051/cocv:2007049. (Pubitemid 351464034)
    • (2008) ESAIM - Control, Optimisation and Calculus of Variations , vol.14 , Issue.2 , pp. 211-232
    • Diening, L.1    Malek, J.2    Steinhauer, M.3
  • 14
    • 23944484056 scopus 로고    scopus 로고
    • Strong solutions for generalized Newtonian fluids
    • DOI 10.1007/s00021-004-0124-8
    • L. DIENING and M. RŮŽIČKA, Strong solutions for generalized Newtonian fluids, J. Math. Fluid Mech. 7 (2005), 413-450. (Pubitemid 41203778)
    • (2005) Journal of Mathematical Fluid Mechanics , vol.7 , Issue.3 , pp. 413-450
    • Diening, L.1    Ruzicka, M.2
  • 16
    • 0013183854 scopus 로고    scopus 로고
    • On existence result for fluids with shear dependent viscosity - unsteady flows
    • W. Jäger, J. Ne?cas, O. John, K. Najzar and J. Stará (eds.) , Chapman and Hall
    • J. FREHSE, J. MÁLEK and M. STEINHAUER, On existence result for fluids with shear dependent viscosity - unsteady flows, In: "Partial Differential Equations", W. Jäger, J. Ne?cas, O. John, K. Najzar and J. Stará (eds.), Chapman and Hall, 2000, 121-129.
    • (2000) Partial Differential Equations , pp. 121-129
    • Frehse, J.1    MáLek, J.2    Steinhauer, M.3
  • 17
    • 0242428236 scopus 로고    scopus 로고
    • On analysis of steady flows of fluids with shear-dependent viscosity based on the Lipschitz truncation method
    • DOI 10.1137/S0036141002410988, PII S0036141002410988
    • J. FREHSE, J. MÁLEK and M. STEINHAUER, On analysis of steady flows of fluids with shear-dependent viscosity based on the Lipschitz truncation method, SIAM J. Math. Anal. 34 (2003), 1064-1083 (electronic). (Pubitemid 37395564)
    • (2003) SIAM Journal on Mathematical Analysis , vol.34 , Issue.5 , pp. 1064-1083
    • Frehse, J.1    Malek, J.2    Steinhauer, M.3
  • 18
    • 0346958328 scopus 로고
    • On stationary incompressiblet Norton fluids and some extensions of Korn's inequality
    • M. FUCHS, On stationary incompressible Norton fluids and some extensions of Korn's inequality, Z. Anal. Anwendungen 13 (1994), 191-197.
    • (1994) Z. Anal. Anwendungen , vol.13 , pp. 191-197
    • Fuchs, M.1
  • 19
    • 0002816568 scopus 로고
    • An introduction to the mathematical theory of the Navier-Stokes equations, Linearized Steady problems
    • Springer, New York
    • G. P. GALDI, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Linearized Steady Problems", Tracts in Natural Philosophy, Vol. 38, Springer, New York, 1994.
    • (1994) Tracts in Natural Philosophy , vol.38
    • Galdi, G.P.1
  • 20
    • 0008661077 scopus 로고
    • On the Stokes problem in Lipschitz domains
    • G. P. GALDI, C. G. SIMADER and H. SOHR, On the Stokes problem in Lipschitz domains, Ann. Mat. Pura Appl. (4) 167 (1994), 147-163.
    • (1994) Ann. Mat. Pura Appl. , vol.4 , Issue.167 , pp. 147-163
    • Galdi, G.P.1    Simader, C.G.2    Sohr, H.3
  • 22
    • 84944818416 scopus 로고
    • Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichugen
    • E. HOPF, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichugen, Math. Nachr. 4 (1951), 213-231.
    • (1951) Math. Nachr. , vol.4 , pp. 213-231
    • Hopf, E.1
  • 24
    • 0036552277 scopus 로고    scopus 로고
    • Very weak solutions of parabolic systems of p-Laplacian type
    • J. KINNUNEN and J. L. LEWIS, Very weak solutions of parabolic systems of p-Laplacian type, Ark. Mat. 40 (2002), 105-132.
    • (2002) Ark. Mat. , vol.40 , pp. 105-132
    • Kinnunen, J.1    Lewis, J.L.2
  • 25
    • 0002859777 scopus 로고
    • New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them
    • O. A. LADYZHENSKAYA, New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc. Steklov Inst. Math. 102 (1967), 95-118.
    • (1967) Proc. Steklov Inst. Math. , vol.102 , pp. 95-118
    • Ladyzhenskaya, O.A.1
  • 29
    • 51249193194 scopus 로고
    • Sur le mouvement d'un liquide visqueux emplissant l'espace
    • J. LERAY, Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta Math. 63 (1934), 193-248.
    • (1934) Acta Math. , vol.63 , pp. 193-248
    • Leray, J.1
  • 31
    • 0011498491 scopus 로고
    • Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer
    • J. MÁLEK, J. NEČAS and A. NOVOTNÝ, Measure-valued solutions and asymptotic behavior of a multipolar model of a boundary layer, Czechoslovak Math. J. 42 (117) (1992), 549-576.
    • (1992) Czechoslovak Math. J. , vol.42 , Issue.117 , pp. 549-576
    • J. Málek1    J. Nečas2    A. Novotný3
  • 34
    • 0000365385 scopus 로고    scopus 로고
    • On weak solutions to a class of non-Newtonian incompressible 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 Incompressible Fluids in Bounded Three-dimensional Domains. The Case p ≥ 2, Adv. Differential Equations 6 (2001), 257-302.
    • (2001) Adv. Differential Equations , vol.6 , pp. 257-302
    • J. Málek1    J. Nečas2    Ružička, M.3
  • 35
    • 66049099719 scopus 로고    scopus 로고
    • Mathematical issues concerning the Navier-Stokes equations and some of its generalizations
    • Elsevier/ North- Holland, Amsterdam
    • J. MÁLEK and K. R. RAJAGOPAL, Mathematical issues concerning the Navier-Stokes equations and some of its generalizations, Handb. Differential Equations, Elsevier/North- Holland, Amsterdam, 2005, 371-459.
    • (2005) Handb. Differential Equations , pp. 371-459
    • J. Málek1    Rajagopal, K.R.2
  • 36
    • 0000034654 scopus 로고
    • Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity
    • J. MÁLEK, K. R. RAJAGOPAL and M. RŮŽIČKA, Existence and regularity of solutions and the stability of the rest state for fluids with shear dependent viscosity, Math. Models Methods Appl. Sci. 5 (1995), 789-812.
    • (1995) Math. Models Methods Appl. Sci. , vol.5 , pp. 789-812
    • J. Málek1    K.R. Rajagopal2    Ružička, M.3
  • 37
    • 0003220990 scopus 로고    scopus 로고
    • Fine regularity of solutions of Elliptic Partial Differential equations
    • American Mathematical Society, Providence, RI
    • J. MALÝ and W. P. ZIEMER, "Fine Regularity of Solutions of Elliptic Partial Differential Equations", Mathematical Surveys and Monographs, Vol. 51, American Mathematical Society, Providence, RI, 1997.
    • (1997) Mathematical Surveys and Monographs , vol.51
    • J. Malý1    Ziemer, W.P.2
  • 39
    • 0242275709 scopus 로고
    • p (Ω) et sur la coercivité des formes formellement positives
    • Montreal
    • p (Ω) et sur la coercivité des formes formellement positives, Séminaire Equations aux Dérivées Partielles, Montreal 317 (1966), 102-128.
    • (1966) Séminaire Equations aux Dérivées Partielles , vol.317 , pp. 102-128
    • J. Nečas1
  • 41
    • 0040822911 scopus 로고
    • Theory of multipolar viscous fluids
    • (Uxbridge, 1990) (London), Academic Press, London
    • J. NEČAS, Theory of multipolar viscous fluids, In: "The Mathematics of Finite Elements and Applications", VII (Uxbridge, 1990) (London), Academic Press, London, 1991, 233-244.
    • (1991) The Mathematics of Finite Elements and Applications , vol.7 , pp. 233-244
    • J. Nečas1
  • 42
    • 0038538865 scopus 로고
    • Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids
    • C. PARÉS, Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids, Appl. Anal. 43 (1992), 245-296.
    • (1992) Appl. Anal. , vol.43 , pp. 245-296
    • C. Parés1
  • 43
    • 34347171922 scopus 로고
    • (p,θ)(ω δ) e loro proprietà
    • (p,θ)(ω δ) e loro proprietà, Ann. Mat. Pura Appl. (4) 69 (1965), 383-392.
    • (1965) Ann. Mat. Pura Appl. , vol.4 , Issue.69 , pp. 383-392
    • Da Prato, G.1
  • 44
    • 0001634191 scopus 로고
    • Mechanics of non-Newtonian fluids
    • G. P. Galdi and J. Ne?cas (eds.), Research Notes in Mathematics Series, Longman
    • K. R. RAJAGOPAL, Mechanics of Non-Newtonian Fluids, In: "Recent Developments in Theoretical Fluid Mechanics", G. P. Galdi and J. Ne?cas (eds.), Research Notes in Mathematics Series, Vol. 291, Longman, 1993, 129-162.
    • (1993) Recent Developments in Theoretical Fluid Mechanics , vol.291 , pp. 129-162
    • Rajagopal, K.R.1
  • 45
    • 0003363431 scopus 로고    scopus 로고
    • Flow of shear dependent electrorheological fluids: Unsteady space periodic case
    • A. Sequeira (ed.), Kluwer/Plenum, New York
    • M. RŮŽIČKA, Flow of shear dependent electrorheological fluids: unsteady space periodic case, In: "Applied Nonlinear Analysis", A. Sequeira (ed.), Kluwer/Plenum, New York, 1999, 485-504.
    • (1999) Applied Nonlinear Analysis , pp. 485-504
    • Ružička, M.1
  • 46
    • 84867942052 scopus 로고    scopus 로고
    • Modeling, mathematical and numerical analysis of electrorheological fluids
    • DOI 10.1007/s10492-004-6432-8
    • M. RŮŽIČKA, Modeling, mathematical and numerical analysis of electrorheological fluids, Appl. Math. 49 (2004), 565-609. (Pubitemid 40041664)
    • (2004) Applications of Mathematics , vol.49 , Issue.6 , pp. 565-609
    • Ruzicka, M.1
  • 47
    • 33846542482 scopus 로고    scopus 로고
    • On extensions of Sobolev functions defined on regular subsets of metric measure spaces
    • P. SHVARTSMAN, On extensions of Sobolev functions defined on regular subsets of metric measure spaces, J. Approx. Theory 144 (2007), 139-161.
    • (2007) J. Approx. Theory , vol.144 , pp. 139-161
    • Shvartsman, P.1
  • 49
    • 0000581771 scopus 로고
    • On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems
    • M. STRUWE, On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems, Manuscripta Math. 35 (1981), 125-145.
    • (1981) Manuscripta Math. , vol.35 , pp. 125-145
    • Struwe, M.1
  • 50
    • 0002565890 scopus 로고
    • The non-linear field theories of mechanics
    • 3, Springer, New York
    • C. TRUESDELL and W. NOLL, "The Non-Linear Field Theories of Mechanics", Handbuch der Physik, Vol. III/3, Springer, New York, 1965.
    • (1965) Handbuch der Physik , vol.3
    • Truesdell, C.1    Noll, W.2
  • 52
    • 33847695734 scopus 로고    scopus 로고
    • Existence of weak solutions to the equations of non-stationary motion of non-Newtonian fluids with shear rate dependent viscosity
    • DOI 10.1007/s00021-006-0219-5
    • J. WOLF, Existence of weak solutions to the equations of nonstationary motion of non-Newtonian fluids with shear-dependent viscosity, J. Math. Fluid Mech. 9 (2007), 104-138. (Pubitemid 46384945)
    • (2007) Journal of Mathematical Fluid Mechanics , vol.9 , Issue.1 , pp. 104-138
    • Wolf, J.1


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