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non-Newtonian fluids; shear dependent viscosity; regularity; Hölder continuity of gradients
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.
[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. MR 1257940 | Zbl 0823.35140
[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
[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.
[4] Lions J.L.: Quelques Méthodes de Résolution des Problèmes aux Limites Non Linéaires. Dunod Paris (1969). MR 0259693 | Zbl 0189.40603
[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
[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
[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
[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.
[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
[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
[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
[12] Temam R.: Navier-Stokes Equations and Nonlinear Functional Analysis. Society for Industrial and Applied Mathematics Philadelphia, Pennsylvania (1995), second edition. Zbl 0833.35110
[13] Ziemer W.P.: Weakly Differentiable Functions. Springer-Verlag New York Inc. (1989). MR 1014685 | Zbl 0692.46022
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