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

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 $\alpha\in (0,1).$