21st Century COE Program : Mathematics of Nonlinear Structure via Singularity

On resolvent of the Stokes equations

There are so many results on the mathematical analysis of the incompressible viscous fluid occupied in the whole space and in the exterior domain when the domain is unbounded. However, there are few results on the problem which domains have noncompact boundaries, except for the case of the half space.

In this talk, we consider the resolvent estimate of the Stokes equation in an infinite layer. As an application, I will state about the unique existence of a global solution to the corresponding nonstationary Navier-Stokes equation and the stability for some exact solutions.