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

Frederic Bernicot (1) , Taoufik Hmidi (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IRMAR - Institut de Recherche Mathématique de Rennes

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

Mots clés: 2D incompressible Euler equations; Global well-posedness; BMO-type space

Domaines: Equations aux dérivées partielles [math.AP]

Frederic Bernicot, Taoufik Hmidi. On the global well-posedness for Euler equations with unbounded vorticity. Dynamics of Partial Differential Equations, 2015, 12 (2), pp.127-155. ⟨hal-00804457⟩