Existence and uniqueness of steady solutions to the incompressible Navier-Stokes problem in two dimensional exterior domain
アブストラクト
In this talk, we discuss the existence of steady 2D exterior Navier-Stokes problem by considering boundary data prescribing a non-trivial flux on the internal boundary. Then, we show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. The method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain.