Weighted Schauder estimates for Evolution Stokes Problem

Abstract

We prove the solvability of the evolution Stokes problem in bounded or exterior domain Ω∈ Rⁿ under the assumption that the initial value of the velocity vector field v₀ belongs to C^s(Ω), $s\in [0,2)$ (in particular, it can be only continuous). The solution is obtained in some weighted Hölder spaces. This result makes it possible to prove the local solvability of a nonlinear problem under the same assumption concerning v₀.

Keywords: Stokes equations, Weighted norms

Mathematics Subject Classification (2000): 35Q30, 76D03