Boussinesq system with measure forcing

2020/01/18 by Piotr B. Mucha, Mucha, Piotr B., Liutang Xue +1
Mathematics · #35Q35 #76D03 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2001.06607

openalex publication_date 2020/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address a question concerning the issue of existence to a Boussinesq type system with a heat source. The problem is studied in the whole two dimensional plane and the heat source is a measure transported by the flow. For arbitrary initial data, we prove global in time existence of unique regular solutions. Measure being a heat source limits regularity of constructing solutions and make us work in a non-standard framework of inhomogeneous Besov spaces of the L^∞(0,T;B^s_p,∞)-type. Application of the Lagrangian coordinates yields uniqueness omitting difficulties with comparison of measures.

Citations

• Compressible Navier-Stokes system : large solutions and incompressible\n limit

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