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

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 \(H^s\) $H^s$ , with \(s < \nicefrac {3}{2}\) $s<\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ , at the vorticity level.