Time periodic solutions for the 2D Euler equation near Taylor-Couette flow

Abstract

In this paper we consider the incompressible 2D Euler equation in an annular domain with non-penetration boundary condition. In this setting, we prove the existence of a family of non-trivially smooth time-periodic solutions at an arbitrarily small distance from the stationary Taylor-Couette flow in $H^s$, with $s<3/2$, at the vorticity level.

76 pages