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L q theory for a generalized Stokes System

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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.

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Authors and Affiliations

  1. Institute of Mathematics, LMU Munich, Theresienstr. 39, 80333, Munich, Germany

    L. Diening

  2. Department of Mathematical Analysis, Charles University in Prague, Sokolovská 83, 186 75, Praha 8, Czech Republic

    P. Kaplický

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  1. L. Diening
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  2. P. Kaplický
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Correspondence to P. Kaplický.

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Diening, L., Kaplický, P. L q theory for a generalized Stokes System. manuscripta math. 141, 333–361 (2013). https://doi.org/10.1007/s00229-012-0574-x

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  • DOI: https://doi.org/10.1007/s00229-012-0574-x

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