On the inviscid Boussinesq system with rough initial data

2014/02/26 by Zineb Hassainia, Taoufik Hmidi, Hassainia, Zineb +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · doi:10.48550/arxiv.1402.6499

openalex publication_date 2014/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data
• On the global well-posedness for Boussinesq system

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