On the global well-posedness for the axisymmetric Euler equations

Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani

Published 2008-01-15Version 1

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.