A Meyers' type estimate for weak solutions to a generalized stationary Navier-Stokes system

Abstract

In this paper, we prove a Meyers' type estimate for weak solutions to a Stokes system with bounded measurable coefficients in place of the usual constant viscosity. Besides the perturbation argument due to Meyers, we make use of the solvability of the classical Stokes problem in $[ W^{ 1,\, q}_{0,\sigma } (\Omega )]^n\, (n=2 \,\, \mbox{or} \,\,n=3, 2< q < 3+\var, \partial \Omega \,\, \mbox{Lipschitz} ).