Abstract
The aim of this paper is to obtain the higher order fractional differentiability of weak solution pairs for the following system modeling the stationary motion of electro-rheological fluids{−div((1+|Du|2)p(x)−22Du)+[∇u]u+∇π=−divFinΩdivu=0inΩ in Besov space, where F is Besov regular and the non-standard growth exponent p(x) is Besov-Orlicz regular. The main approach to prove this result is to establish a Besov regular priori estimate of weak solution pairs for its Stokes setting without convective term [∇u]u, and then treat the convective term as a part of nonhomogeneous term in the general systems.
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