Tongkeun Chang

On maximum modulus estimates of the navier–stokes equations with nonzero boundary data

We consider discontinuous influx for the Navier--Stokes flow and construct a solution that is unbounded in a neighborhood of a discontinuous point of given bounded boundary data for any dimension l...

Solvability for Stokes System in Hölder Spaces in Bounded domains and Its Applications

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 We also construct an example, which shows that Hölder continuity is no longer valid, unless the proposed condition of boundary data is fulfilled.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.