Calculus of Variations and Geometric Measure Theory
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E. Acerbi - G. Mingione

Regularity results for electrorheological fluids: the stationary case

created on 30 Nov 2001
modified on 06 Jul 2002

[BibTeX]

Published Paper

Inserted: 30 nov 2001
Last Updated: 6 jul 2002

Journal: C. R. Acad. Sci. Paris Sér. I Math.
Volume: 334
Number: 9
Pages: 817-822
Year: 2002

Abstract:

We report on recent regularity results for stationary electrorheological fluids, as modeled by Rajagopal and Ruzicka. The results cover the Stokes type system: $$ - div ((1+
D(u)
{2}){(p(E)-2)2}D(u)) +D\pi= - div (u \otimes u) +f; \ \ \ \ \ div u=0 $$ $$ div E =0;\ \ \ \ \ \ \ \ \ curl E=0$$ where $u$ is the velocity, $\pi$ the pressure, $D(u)$ the symmetric part of the gradient $\nabla u$ and $E$ the electromagnetic field. Regularity results for $\nabla u$ are obtained provided $p(E) >9/5$. The full proofs are contained in our paper: "Regularity results for stationary electrorheological fluids" (to appear on Arch. Rational Mech. Anal.).

Keywords: regularity, Non Newtonian Fluids, Korn Inequalities, Non standard growth

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