On the global well-posedness for the axisymmetric Euler equations

TL;DR

This paper investigates the global well-posedness of 3D axisymmetric Euler equations with initial data in critical Besov spaces, introducing a new vorticity decomposition to address the limitations of the BKM criterion.

Contribution

It presents a novel approach using vorticity decomposition to establish well-posedness without relying on the BKM criterion for critical Besov space initial data.

Findings

Proves global well-posedness under new conditions

Introduces a new vorticity decomposition method

Circumvents limitations of the BKM criterion

Abstract

This paper deals with the global well-posedness of the 3D axisymmetric Euler equations for initial data lying in critical Besov spaces $B_{p,1}^{1+3/p}$. In this case the BKM criterion is not known to be valid and to circumvent this difficulty we use a new decomposition of the vorticity.