Stationary Stokes and Navier–Stokes Systems on Two- or Three-Dimensional Domains with Corners. Part I. Linearized Equations

Abstract

The $H^s $-regularity (s being real and nonnegative) of solutions of the Stokes system in domains with corners is studied. In particular, a $H^2 $-regularity result on a convex polyhedron that generalizes Kellogg and Osborn’s result on a convex polygon to three-dimensional domains is stated. Sharper regularity on a cube and on other domains with corners is attained. Conditions for the problem to be Fredholm are also given, and its singular functions along with those of the nonlinear problem are studied in the second part of this paper.