We consider Stokes system in bounded convex domains and we present conditions of given data, in particular, boundary data, which ensure Hölder continuity of solutions. For Hölder continuous solutions for the Stokes system the normal component of boundary data requires a bit more regular than boundary data of Hölder continuous solutions for the heat equation. We also construct an example, which shows that Hölder continuity is no longer valid, unless the proposed condition of boundary data is fulfilled. As an application, we consider a certain general types of nonlinear systems coupled to fluid equations and local well-posedness is established in Hölder spaces.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics