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Leray's plane steady state solutions are nontrivial
Advances in Mathematics ( IF 1.5 ) Pub Date : 2021-01-01 , DOI: 10.1016/j.aim.2020.107451
Mikhail V. Korobkov , Konstantin Pileckas , Remigio Russo

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.

中文翻译:

Leray 的平面稳态解很重要

我们研究了在二维外部域(流过指定物体)中静止 Navier-Stokes 系统障碍问题的解决方案。我们证明了这个问题的经典 Leray 解总是不平凡的。不假设附加条件(对称或小等)。这是 CJ Amick (Acta Math. 1988) 的经典结果的完整扩展,其中在对称假设下证明了非平凡性。
更新日期:2021-01-01
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