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

TL;DR

This paper investigates the behavior of vorticity in high-dimensional bi-rotational Euler flows, demonstrating that certain initial conditions lead to infinite support growth, revealing new dynamics in fluid flow theory.

Contribution

It introduces a novel analysis of vorticity growth in high-dimensional Euler equations with bi-rotational symmetry, highlighting infinite support expansion for patch initial data.

Findings

Support diameter grows infinitely over time.

Vorticity dynamics in high dimensions differ from classical 3D cases.

New insights into high-dimensional fluid flow behavior.

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.