On the inviscid Boussinesq system with rough initial data

Zineb Hassainia (1) , Taoufik Hmidi (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We deal with the local well-posedness theory for the two-dimensional inviscid Boussinesq system with rough initial data of Yudovich type. The problem is in some sense critical due to some terms involving Riesz transforms in the vorticity-density formulation. We give a positive answer for a special sub-class of Yudovich data including smooth and singular vortex patches. For the latter case we assume in addition that the initial density is constant around the singular part of the patch boundary.

Mots clés: 2D inviscid Boussinesq system; vortex patches; local well-posedness

Domaines: Equations aux dérivées partielles [math.AP]

Zineb Hassainia, Taoufik Hmidi. On the inviscid Boussinesq system with rough initial data. Journal of Mathematical Analysis and Applications, 2015, 430 (2), pp.777-809. ⟨10.1016/j.jmaa.2015.04.087⟩. ⟨hal-00954541⟩