Existence of weak solutions for steady flows of electrorheological fluid with Navier-slip type boundary conditions - Cholmin Sin; Sin-Il Ri (Mathematica Bohemica, 2022)
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 Poincaré- and Korn-type inequalities, and then construct Lipschitz truncation functions preserving the zero normal component in variable exponent Sobolev spaces.