Estimates for the navier-stokes equations in the half-space for nonlocalized data

Abstract

This paper is devoted to the study of the Stokes and Navier-Stokes equations, in a half-space, for initial data in a class of locally uniform Lebesgue integrable functions, namely Lquloc, σ (Rd+). We prove the analyticity of the Stokes semigroup e-t A in Lquloc, σ (Rd+) for 1 < q ≤∞. This follows from the analysis of the Stokes resolvent problem for data in Lquloc, σ (Rd+),