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：

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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。