Support growth of vorticity for bi-rotational Euler flows in high dimensions

Abstract

We study incompressible Euler equations in ${\mathbb{R}}^d$ with $d\ge 4$ under bi-rotational symmetry without swirl, which reduces the Euler equations to a scalar vorticity advection in the first quadrant. We show that patch type initial vorticities exhibit infinite growth of the support diameter.

arXiv comment13 pages