Steady compressible Navier--Stokes equations in domains with non-compact boundaries

Abstrakt

We consider the steady compressible Navier--Stokes equations of isentropic flow in three-dimensional domains with several exits to infinity with prescribed pressure drops. On the one hand, when each exit is supposed to contain a cone inside, we shall construct bounded energy weak solution for adiabatic constant $\gamma gt 3$.

On the other hand, when the exits do not open sufficiently rapidly, we shall prove a non-existence result.