On the inviscid Boussinesq system with rough initial data

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 s...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-10, Vol.430 (2), p.777-809
Main Authors: Hassainia, Zineb, Hmidi, Taoufik
Format: Article
Language:English
Subjects:
2D inviscid Boussinesq system
Analysis of PDEs
Local well-posedness
Mathematics
Vortex patches
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Summary: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.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2015.04.087