The inviscid inflow-outflow problem via analyticity

Abstract

We consider the incompressible Euler equations on an analytic domain \(\Omega \) with a nonhomogeneous boundary condition \(u\cdot {\textsf{n}} = {\overline{u}}\cdot {\textsf{n}}\) on \(\partial \Omega \), where \({\overline{u}}\) is a given divergence-free analytic vector field. We establish the local well-posedness for u in analytic spaces without any compatibility conditions in all space dimensions. We also prove the global well-posedness in the 2D case if \({\overline{u}}\) decays in time sufficiently fast.