The inviscid inflow-outflow problem via analyticity

Abstract

We consider the incompressible Euler equations on an analytic domain Ω with a nonhomogeneous boundary condition u·n=u¯·n on ∂Ω, where 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 u¯ decays in time sufficiently fast.