# American Institute of Mathematical Sciences

March  2008, 1(1): 41-50. doi: 10.3934/dcdss.2008.1.41

## Incompressible fluids with shear rate and pressure dependent viscosity: Regularity of steady planar flows

 1 Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 186 75 Prague 8 2 Charles University, Faculty of Mathematics and Physics, Department of Mathematical Analysis, Sokolovská 83, 186 75 Prague 8, Czech Republic

Received  September 2006 Revised  March 2007 Published  December 2007

We study the regularity of steady planar flow of fluids where the shearing stress may depend on the symmetric part of the velocity vector field and the pressure. For simplicity the periodic boundary conditions are considered. Using Meyers estimates we show that there exists a solution which is smooth. In the case where it is allowed to test weak formulation of the problem with a weak solution we prove regularity of all weak solutions.
Citation: M. Bulíček, P. Kaplický. Incompressible fluids with shear rate and pressure dependent viscosity: Regularity of steady planar flows. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 41-50. doi: 10.3934/dcdss.2008.1.41
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