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Regularity results for stationary electro-rheological fluids. (English) Zbl 1038.76058
Summary: We prove regularity results for weak solutions to systems modelling electro-rheological fluids in the stationary case; a particular case of the system we consider is \(\text{div\,} u = 0\), \(-\text{div}\bigl((1+| \mathcal E(u)| ^{2})^{(p(x)-2)/2}\mathcal E(u)\bigr)+ D \pi = f(x,u,Du),\) where \(\mathcal E(u)\) is the symmetric part of the gradient \(Du\), and the variable growth exponent \(p(x)\) is a Hölder continuous function larger than \(3n/(n+2)\).

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
76A05 Non-Newtonian fluids
35Q35 PDEs in connection with fluid mechanics
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