Some remarks on steady solutions to the Euler system in ℝ^d

2020/12/10 by Francesco Fanelli, Eduard Feireisl, Fanelli, Francesco +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2012.05994

Submitted

arxiv created 2020/12/10 · arxiv updated 2020/12/14

Abstract

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.

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