Weighted Schauder estimates for evolution Stokes problem (Q867738)

The author proves the solvability of the evolution Stokes problem in a connected bounded or exterior domain \(\Omega \subset\mathbb R^n\) under the assumption that the initial value of the velocity vector field \(v_0\) belongs to \(C^s (\Omega )\), \(s\in [0,2]\) (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 \(v_0\).