Full regularity of weak solutions to a class of nonlinear fluids in two dimensions - stationary, periodic problem

Commentationes Mathematicae Universitatis Carolinae

Volumn 38, Issue 4, 1997, Pages 681-695

  Kaplický, Petr ^a   Málek, Josef ^b   Stará, Jana ^a  

^a Department of Mathematical Analysis ^*  (Czech Republic)

^b CHARLES UNIVERSITY   (Czech Republic)

Author keywords

H lder continuity of gradients; Non Newtonian fluids; Regularity; Shear dependent viscosity

Indexed keywords

EID: 0009042484     PISSN: 00102628     EISSN: 12137243     Source Type: Journal    
DOI: None     Document Type: Article

References (13)

1. Amrouche Ch., Girault V., Decomposition of vector spaces and application to the Stokes problem in arbitrary dimension, Czechoslovak Math. J. 44 (1994), 109-141
2. Bojarski B.V., Generalized solutions to first order systems of elliptic type with discontin-uous coefficients (in Russian), Mat. Sbornik 43 (1957), 451-503
3. Frehse J., Málek J., Steinhauer M., An Existence Result for Fluids with Shear Depen-dent Viscosity-Steady Flows, accepted to the Proceedings of the Second World Congress of Nonlinear Analysts
4. Lions J.L., Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires, Dunod, Paris, 1969
5. Málek J., Nečas J., Ružička M., On weak solutions to a class of non-Newtonian Incompress-ible fluids in bounded three-dimensional domains. The case p ≥ 2, submitted to Advances in Differential Equations, Preprint SFB 256, No. 481 (1996)
6. Málek J., Rajagopal K.R., Ružička M., Existence and regularity of solutions and stability of the rest state for fluids with shear dependent viscosity, Mathematical Models and Methods in Applied Sciences 6 (1995), 789-812
7. Meyers N.G., On Lp estimates for the gradient of solutions of second order elliptic diver-gence equations, Annali della Scuola Normale Superiore di Pisa 17 (1963), 189-206
8. Nečas J., Sur les normes équivalentes dans Wk,p(Ω) et sur la coercivité des formes formelle-ment positives, Les Presses de l'Université de Montréal, Montréal, 1996, pp. 102-128
9. Nečas J., Sur la régularité des solutions faibles des équations elliptiques non linéaires, Comment. Math. Univ. Carolinae 9.3 (1968), 365-413
10. Nečas J., Sur la régularité des solutions variationnelles des équations elliptiques non-linéaires d'ordre 2k en deux dimensions, Annali della Scuola Normale Superiore di Pisa XXI Fasc. III (1967), 427-457
11. Stará J., Regularity results for non-linear elliptic systems in two dimensions, Annali della Scuola Normale Superiore di Pisa XXV Fasc. I (1971), 163-190
12. Temam R., Navier-Stokes Equations and Nonlinear Functional Analysis, Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, 1995, second edition
13. Ziemer W.P., Weakly Differentiable Functions, Springer-Verlag, New York Inc., 1989