On the global well-posedness of the Euler–Boussinesq system with fractional dissipation

We study the global well-posedness of the Euler–Boussinesq system with the term dissipation | D | α on the temperature equation. We prove that for α > 1 the coupled system has a global unique solution for initial data with critical regularities.

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Bibliographic Details
Published in:Physica. D 2010-08, Vol.239 (15), p.1387-1401
Main Authors: Hmidi, T., Zerguine, M.
Format: Article
Language:English
Subjects:
Analysis of PDEs
Besov spaces
Dissipation
Euler–Boussinesq system
Exact sciences and technology
Mathematical analysis
Mathematics
Nonlinear phenomena
Paradifferential calculus
Physics
Regularity
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Description
Summary:We study the global well-posedness of the Euler–Boussinesq system with the term dissipation | D | α on the temperature equation. We prove that for α > 1 the coupled system has a global unique solution for initial data with critical regularities.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2009.12.009