Some remarks on steady solutions to the Euler system in ${\mathbb{R}}^d$

Abstract

We show that the Euler system of gas dynamics in ${\mathbb{R}}^d$, $d=2,3$, with positive far field density and arbitrary far field entropy, admits infinitely many steady solutions with compactly supported velocity. The same proof yields a similar result for the incompressible Euler system with variable density. In particular, these are examples of global in time smooth (non-trivial) solutions for the corresponding time-dependent systems.

Submitted