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arXiv · 1911.11546

Leray's plane steady state solutions are nontrivial

Mikhail Korobkov·Konstantin Pileckas·Remigio Russo
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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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Mikhail Korobkov, Konstantin Pileckas, Remigio Russo. 2019-11-26. Leray's plane steady state solutions are nontrivial. https://arxiv.org/abs/1911.11546

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