On the global well-posedness for the axisymmetric Euler equations

Hammadi Abidi (1) , Taoufik Hmidi (1) , Sahbi Keraani

1 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Domaines: Equations aux dérivées partielles [math.AP]

Hammadi Abidi, Taoufik Hmidi, Sahbi Keraani. On the global well-posedness for the axisymmetric Euler equations. Mathematische Annalen, 2010, 347 (1), pp.15-41. ⟨10.1007/s00208-009-0425-6⟩. ⟨hal-00521722⟩