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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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