Electron. J. Diff. Equ., Vol. 2014 (2014), No. 70, pp. 1-20.

Regularity of planar flows for shear-thickening fluids under perfect slip boundary conditions

Jakub Tichy

For evolutionary planar flows of shear-thickening fluids in bounded domains we prove the existence of a solution with the Holder continuous velocity gradients and pressure. The problem is equipped with perfect slip boundary conditions. We also show L^q theory result for Stokes system under perfect slip boundary conditions.

Submitted April 19, 2013. Published March 15, 2014.
Math Subject Classifications: 35B65, 35K51, 35Q35, 76D03.
Key Words: Generalized Newtonian fluid; regularity; perfect slip boundary conditions.

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Jakub Tichý
Charles University in Prague
Department of Mathematical Analysis
Sokolovská 83, 186 75 Praha 8, Czech Republic
email: jakub.tichy@fit.cvut.cz

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