Elliptic and Parabolic Equations - Abstract

Köhne, Matthias

On natural and artificial boundary conditions for incompressible Newtonian flows

We derive a class of boundary conditions for incompressible Newtonian flows, which in the homogeneous case are neutral w.r.t. to the energy balance. These conditions prescribe certain boundary data composed of velocity, vorticity, normal viscous stress and pressure. We study the local well-posedness of the Navier--Stokes equations subject to such boundary conditions in an $L_p$-setting as well as the possibility to combine two different conditions on two orthogonal parts of the boundary.
This is a joint work with Dieter Bothe and Jan Prüß.