Infinite growth in vorticity gradient of compactly supported planar vorticity near Lamb dipole. (June 2022) - Choi, Kyudong
Abstract: We prove linear in time filamentation for perturbations of the Lamb dipole, which is a traveling wave solution to the incompressible Euler equations in R 2 . The main ingredient is a recent nonlinear orbital stability result by Abe–Choi. As a consequence, we obtain linear in time growth for the vorticity gradient for all times, for certain smooth and compactly supported initial vorticity in R 2 . The construction carries over to some generalized SQG equations.