Besov regularity theory for stationary electrorheological fluids

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 + vertical bar Du vertical bar(2)) (p(x)-2/2) Du) + [del u]u + del pi = -div F in Omega div u = 0 in Omega 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 [del u]u, and then treat the convective term as a part of nonhomogeneous term in the general systems. (c) 2022 Elsevier Inc. All rights reserved.