Leray's plane steady state solutions are nontrivial

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 (1988) [1] where nontriviality was proved under symmetry assumption.