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L-q theory for a generalized Stokes System

Publication at Faculty of Mathematics and Physics |
2013

Abstract

Regularity properties of solutions to the stationary generalized Stokes system are studied. The extra stress tensor is assumed to have a growth given by some N-function, which includes the situation of p-growth.

We show results about differentiability of weak solutions. As a consequence we obtain the gradient L (q) estimates for the problem.

These estimates are applied to the stationary generalized Navier Stokes equations.