The 3D incompressible Euler equations in a bounded domain are most often supplemented with impermeable boundary conditions, which constrain the fluid to neither enter nor leave the domain. In this talk, I will explain how we obtain well-posedness of solutions in which the full value of the velocity is specified on inflow and the normal component is specified on outflow. We do this for multiply connected domains, and establish compatibility conditions to obtain arbitrarily high Holder regularity.

This is joint work with Gung-Min Gie and Anna Mazzucato.