Leray's plane steady state solutions are nontrivial
Analysis of PDEs
2019-11-27 v1
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.
Keywords
Cite
@article{arxiv.1911.11546,
title = {Leray's plane steady state solutions are nontrivial},
author = {Mikhail Korobkov and Konstantin Pileckas and Remigio Russo},
journal= {arXiv preprint arXiv:1911.11546},
year = {2019}
}