Nonlinear stability of sinusoidal Euler flows on a flat two-torus

Sinusoidal flows are important explicit stationary solutions of the incompressible Euler equation on a flat two-torus. In this paper, we prove that sinusoidal flows related to least eigenfunctions of the negative Laplacian are, up to phase translations, nonlinearly stable under L^p norm of the vorticity for any 1更多