Calculus of Variations and Geometric Measure Theory
home | mail | papers | authors | news | seminars | events | open positions | login

E. Acerbi - G. Mingione

Regularity results for stationary electro-rheological fluids

created on 30 Nov 2001
modified on 22 Oct 2002

[BibTeX]

Published Paper

Inserted: 30 nov 2001
Last Updated: 22 oct 2002

Journal: Arch. Ration. Mech. Anal.
Volume: 164
Number: 3
Pages: 213-259
Year: 2002

Abstract:

We prove 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. Note that the interaction between the fluid and the electromagnetic field $E$ is described via the variable growth exponent $p(
E
).$ Hölder continuity results for $\nabla u$ are obtained provided $p(E) >9/5$.

Keywords: regularity, Non Newtonian Fluids, Korn Inequalities

Credits | Cookie policy | HTML 5 | CSS 2.1