Leray's plane steady state solutions are nontrivial

2019/11/26 by Korobkov, Mikhail, Pileckas, Konstantin, Russo, Remigio
#35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1911.11546

Abstract

We study solutions to the obstacle problem for the stationary Navier--Stokes system in a~two dimensional exterior domain (flow past a prescribed body). We prove that the classical Leray solution to this problem is always nontrivial. No additional condition (on symmetry or smallness, etc.) is assumed. This is a complete extension of a~classical result of C.J. Amick (Acta Math. 1988) where nontriviality was proved under symmetry assumption.

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