A weighted setting for the stationary Navier Stokes equations under singular forcing

Abstract

In two dimensions, we show existence of solutions to the stationary Navier Stokes equations on weighted spaces ${\mathbf{H}}_0^1(\omega ,\Omega )\times L^2(\omega ,\Omega )$, where the weight belongs to the Muckenhoupt class $A_2$. We show how this theory can be applied to obtain a priori error estimates for approximations of the solution to the Navier Stokes problem with singular sources.