On the analysis and approximation of some models of fluids over weighted spaces on convex polyhedra

Abstract

We study the Stokes problem over convex polyhedral domains on weighted Sobolev spaces. The weight is assumed to belong to the Muckenhoupt class \(\varvec{A}_{\varvec{q}}\) for \(\varvec{q} \in (1,\varvec{\infty })\). We show that the Stokes problem is well-posed for all \(\varvec{q}\). In addition, we show that the finite element Stokes projection is stable on weighted spaces. With the aid of these tools, we provide well-posedness and approximation results to some classes of non-Newtonian fluids.