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Digital Object Identifier (DOI) 10.1007/s00205-002-0208-7 Arch. Rational Mech. Anal. 164 (2002) 213259
 

Summary: Digital Object Identifier (DOI) 10.1007/s00205-002-0208-7
Arch. Rational Mech. Anal. 164 (2002) 213­259
Regularity Results for Stationary
Electro-Rheological Fluids
Emilio Acerbi & Giuseppe Mingione
Communicated by V. Sverák
Abstract
We prove regularity results for weak solutions to systems modelling electro-
rheological fluids in the stationary case, as proposed in [27,31]; a particular case
of the system we consider is
div u = 0, - div (1 + |E(u)|2
)(p(x)-2)/2
E(u) + D = f (x, u, Du),
where E(u) is the symmetric part of the gradient Du and the variable growth
exponent p(x) is a H¨older continuous function larger than 3n/(n + 2).
1. Introduction
In recent years increasing attention has been paid to the study of electro-
rheological fluids; these are particular fluids of high technological interest, possess-
ing the ability to change, sometimes in a dramatic way, their mechanical properties
when in the presence of an electromagnetic field E (their viscosity may vary by a

  

Source: Acerbi, Emilio - Dipartimento di Matematica, Universitŕ degli Studi di Parma

 

Collections: Mathematics