Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions

Abstract

We prove the existence of weak solutions for steady flows of electrorheological fluids with homogeneous Navier-slip type boundary conditions provided p(x) > 2n/(n+2). To prove this, we show Poincaréand Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.