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Existence of local strong solutions for motions of electrorheological fluids in three dimensions. (English) Zbl 1122.76092
Summary: We prove for three-dimensional domains the existence of local strong solutions to systems of nonlinear partial differential equations with \(p(\cdot\))-structure, \(p_{\infty} \leq p(\cdot)\leq p_{0}\), and Dirichlet boundary conditions for \(p_{\infty} > \frac {9}{5}\) without restriction on the upper bound \(p_{0}\). In particular, this result is applicable to the motion of electrorheological fluids.

MSC:
76W05 Magnetohydrodynamics and electrohydrodynamics
35Q35 PDEs in connection with fluid mechanics
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