English

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}
}