Dynamics of Partial Differential Equations

Volume 12 (2015)

Number 2

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

Pages: 127 – 155

DOI: https://dx.doi.org/10.4310/DPDE.2015.v12.n2.a3


Frédéric Bernicot (Laboratoire de Mathématiques, CNRS, Université de Nantes, France)

Taoufik Hmidi (IRMAR, Université de Rennes 1, Campus de Beaulieu, Rennes, France)


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


2D incompressible Euler equations, Global well-posedness, BMO-type space

2010 Mathematics Subject Classification

35Q35, 76B03

Published 9 June 2015