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

Francesco Fanelli (1, 2) , Eduard Feireisl

1 EDPA - Équations aux dérivées partielles, analyse
2 ICJ - Institut Camille Jordan

We show that the Euler system of gas dynamics in 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.

Mots clés: Euler system; non-homogeneous fluid; steady solution; far field conditions

Domaines: Equations aux dérivées partielles [math.AP]

Francesco Fanelli, Eduard Feireisl. Some remarks on steady solutions to the Euler system in $\mathbb{R}^d$. Applied Mathematics Letters, 2021, 116, ⟨10.1016/j.aml.2021.107031⟩. ⟨hal-03060529⟩