| Title:
|
Full regularity of weak solutions to a class of nonlinear fluids in two dimensions -- stationary, periodic problem (English) |
| Author:
|
Kaplický, Petr |
| Author:
|
Málek, Josef |
| Author:
|
Stará, Jana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
38 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
681-695 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the existence of regular solution to a system of nonlinear equations describing the steady motions of a certain class of non-Newtonian fluids in two dimensions. The equations are completed by requirement that all functions are periodic. (English) |
| Keyword:
|
non-Newtonian fluids |
| Keyword:
|
shear dependent viscosity |
| Keyword:
|
regularity |
| Keyword:
|
Hölder continuity of gradients |
| MSC:
|
35D10 |
| MSC:
|
35J65 |
| MSC:
|
35Q35 |
| MSC:
|
76A05 |
| MSC:
|
76F10 |
| idZBL:
|
Zbl 0946.76006 |
| idMR:
|
MR1603694 |
| . |
| Date available:
|
2009-01-08T18:37:17Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118966 |
| . |
| Reference:
|
[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. Zbl 0823.35140, MR 1257940 |
| Reference:
|
[2] Bojarski B.V.: Generalized solutions to first order systems of elliptic type with discontinuous coefficients (in Russian).Mat. Sbornik 43 (1957), 451-503. MR 0106324 |
| Reference:
|
[3] Frehse J., Málek J., Steinhauer M.: An Existence Result for Fluids with Shear Dependent Viscosity-Steady Flows.accepted to the Proceedings of the Second World Congress of Nonlinear Analysts. |
| Reference:
|
[4] Lions J.L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires.Dunod Paris (1969). Zbl 0189.40603, MR 0259693 |
| Reference:
|
[5] Málek J., Nečas J., Růžička M.: On weak solutions to a class of non-Newtonian Incompressible fluids in bounded three-dimensional domains. The case $p\ge 2$.submitted to {Advances in Differential Equations}, Preprint SFB 256, No. 481 (1996). MR 1389407 |
| Reference:
|
[6] Málek J., Rajagopal K.R., Růžička 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. MR 1348587 |
| Reference:
|
[7] Meyers N.G.: On $L_p$ estimates for the gradient of solutions of second order elliptic divergence equations.Annali della Scuola Normale Superiore di Pisa 17 (1963), 189-206. MR 0159110 |
| Reference:
|
[8] Nečas J.: Sur les normes équivalentes dans $W^{k,p}(Ømega)$ et sur la coercivité des formes formellement positives.Les Presses de l'Université de Montréal, Montréal, 1996, pp. 102-128. |
| Reference:
|
[9] Nečas J.: Sur la régularité des solutions faibles des équations elliptiques non linéaires.Comment. Math. Univ. Carolinae 9.3 (1968), 365-413. MR 0241804 |
| Reference:
|
[10] Nečas J.: Sur la régularité des solutions variationnelles des équations elliptiques nonlinéaires d'ordre $2k$ en deux dimensions.Annali della Scuola Normale Superiore di Pisa XXI Fasc. III (1967), 427-457. MR 0226467 |
| Reference:
|
[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. MR 0299935 |
| Reference:
|
[12] Temam R.: Navier-Stokes Equations and Nonlinear Functional Analysis.Society for Industrial and Applied Mathematics Philadelphia, Pennsylvania (1995), second edition. Zbl 0833.35110 |
| Reference:
|
[13] Ziemer W.P.: Weakly Differentiable Functions.Springer-Verlag New York Inc. (1989). Zbl 0692.46022, MR 1014685 |
| . |
