Weak solutions for steady, fully inhomogeneous generalized Navier-Stokes equations

Abstract

We consider the question of existence of weak solutions for the fully inhomogeneous, stationary generalized Navier–Stokes equations for homogeneous, shear-thinning fluids. For a shear rate exponent $p\in \left(\frac{2d}{d+1},2\right)$, previous results require either smallness of the norm or vanishing of the normal component of the boundary data. In this work, combining previous methods, we propose a new, more general smallness condition.