On the global well-posedness for Euler equations with unbounded vorticity

TL;DR

This paper proves the global persistence of vorticity in certain unbounded function spaces for 2D Euler equations, showing velocity fields can be less regular than Lipschitz but still maintain well-posedness.

Contribution

It establishes global well-posedness results for 2D Euler equations with unbounded vorticity in weighted Morrey-Campanato spaces, extending previous regularity frameworks.

Findings

Vorticity propagates globally in weighted Morrey-Campanato spaces.

Velocity fields belong to the log-Lipschitz class, not necessarily Lipschitz.

Results extend well-posedness to unbounded vorticity scenarios.

Abstract

In this paper, we are interested in the global persistence regularity for the 2D incompressible Euler equations in some function spaces allowing unbounded vorticities. More precisely, we prove the global propagation of the vorticity in some weighted Morrey-Campanato spaces and in this framework the velocity field is not necessarily Lipschitz but belongs to the log-Lipschitz class $L^\alpha L,$ for some $\alpha\in (0,1).$