Strong solutions for generalized Newtonian fluids

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue 3, 2005, Pages 413-450

  Diening, Lars ^a   Růžička, Michael ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

Electrorheological fluids; Existence of generalized solutions of PDE; Non Newtonian fluid flow; Parabolic interpolation; Regularity of generalized solutions of PDE

Indexed keywords

BOUNDARY CONDITIONS; RHEOLOGY; SOLUTIONS; STRESS ANALYSIS; TENSORS; THREE DIMENSIONAL;

ELECTRORHEOLOGICAL FLUIDS; EXISTENCE OF GENERALIZED SOLUTIONS OF PDE; NON-NEWTONIAN FLUID FLOW; PARABOLIC INTERPOLATION; REGULARITY OF GENERALIZED SOLUTIONS OF PDE;

NEWTONIAN FLOW;

BOUNDARY CONDITIONS; ELECTRORHEOLOGICAL FLUID; FLUID FLOW; NEWTONIAN FLUID;

FLUID FLOW; NEWTONIAN FLUID;

EID: 23944484056     PISSN: 14226928     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00021-004-0124-8     Document Type: Article

References (27)

1. R. A. ADAMS, Sobolev spaces, Pure and Applied Mathematics, Vol. 65, Academic Press, New York-London, 1975.
2. H. BELLOUT, F. BLOOM and J. NEČAS, Young measure-valued solutions for non-Newtonian incompressible fluids, Commun. Partial Differ. Equations 19 (1994), 1763-1803.
3. J. BERGH and J. LÖFSTRÖM, Interpolation spaces. An introduction, Grundlehren der Mathematischen Wissenschaften, No. 223, Springer-Verlag, Berlin, 1976.
4. L. DIENING, Theoretical and numerical results for electrorheological fluids, PhD thesis, Univ. Freiburg im Breisgau, Mathematische Fakultät, 156 p. , 2002.
5. p(·) and problems related to fluid dynamics, Journal für die Reine und Angewandte Mathematik, accepted, 2003.
6. J. DIESTEL and J. J. JUN. UHL, Vector Measures, Number 15 in Mathematical Surveys, American Mathematical Society, 1977.
7. J. FREHSE, J. MÁLEK and M. STEINHAUER, On existence results for fluids with shear dependent viscosity - unsteady flows, in: Partial differential equations (Praha, 1998), volume 406 of Chapman & Hall/CRC Res. Notes Math., pages 121-129. Chapman & Hall/CRC, Boca Raton, FL, 2000.
8. J. FREHSE, J. MÁLEK and M. STEINHAUER, An existence result for fluids with shear dependent viscosity - steady flows, in: Proceedings of the Second World Congress of Nonlinear Analysts, Part 5 (Athens, 1996), volume 30, pages 3041-3049, 1997.
9. M. GIAQUINTA, G. MODICA and J. SOUČEK, Cartesian Currents in the Calculus of Variations II, volume 38 of A Series of Modern Surveys in Mathematics. Springer, 1998.
10. P. KAPLICKÝ, J. MÁLEK and J. STARÁ, Full regularity of weak solutions to a class of nonlinear fluids in two dimensions - stationary, periodic problem, Commentat. Math. Univ. Carol. 38 (1997), 681-695.
11. 1,α-solutions to a class of nonlinear fluids in two dimensions-stationary Dirichlet problem, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 259
12. (Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Tear. Punkts. 30) 297 (1999), 89-121.
13. k,p(x) Czechoslovak Math. J. 41 (116) (1991), 592-618.
14. O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flow, Gordon and Breach Science Publishers, New York - London - Paris, XVIII, 224 p., 1969.
15. J. L. LIONS and JAAK PEETRE, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math. 19 (1964), 5-68.
16. J. L. LIONS, Quelques méthodes de résolution des problèmes aux limites non linéaires, Études mathématiques, XX, 554 p. Dunod; Gauthier-Villars, Paris, 1969.
17. J. MÁLEK, J. NECAS, M. ROKYTA and M. RŮŽIČKA, Weak and measure-valued solutions to evolutionary PDEs, Chapman & Hall, London, 1996.
18. J. MÁLEK, J. NEČAS and M. RŮZIČKA, On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains: The case p ≥ 2, Adv. Differ. Equ. 6 (2001), 257-302.
19. 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.
20. J. MÁLEK, J. NEČAS and M. RŮŽIČKA, On the non-Newtonian incompressible fluids, Math. Models Methods Appl. Sci. 3 (1993), 35-63.
21. A. PROHL and M. RŮŽIČKA, On fully implicit space-time discretization for motions of incompressible fluids with shear dependent viscosities: the case p ≤ 2, SIAM J. Num. Anal. 39 (2001), 214-249.
22. K. R. RAJAGOPAL and M. RŮŽIČKA, On the modeling of electrorheological materials, Mech. Res. Commun. 23 (1996), 401-407.
23. K. R. RAJAGOPAL and M. RŮŽIČKA, Mathematical modeling of electrorheological materials, Cont. Mech. and Thermodyn. 13 (2001), 59-78.
24. M. RŮŽIČKA, A note on steady flow of fluids with shear dependent viscosity, Nonlinear Anal., Theory Methods Appl. 30 (1997), 3029-3039.
25. M. RŮŽIČKA, Flow of shear dependent electrorheological fluids: unsteady space periodic case, in: Applied nonlinear analysis, pp. 485-504, Kluwer/Plenum, New York, 1999.
26. M. RŮŽIČKA, Electrorheological fluids: modeling and mathematical theory, volume 1748 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 2000.
27. H. TRIEBEL, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978.