Existence of local strong solutions for motions of electrorheological fluids in three dimensions

We prove for three-dimensional domains the existence of local strong solutions to systems of nonlinear partial differential equations with p(⋅)p(⋅)-structure, p∞≤p(⋅)≤p0p∞≤p(⋅)≤p0, and Dirichlet boundary conditions for p∞>95 without restriction on the upper bound p0p0. In particular this result is applicable to the motion of electrorheological fluids.