On a maximum principle and its application to the logarithmically critical boussinesq system

Taoufik Hmidi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we study a transport-diffusion model with some logarithmic dissipations. We look for two kinds of estimates. The first is a maximum principle whose proof is based on Askey theorem concerning characteristic functions and some tools from the theory of C0-semigroups. The second is a smoothing effect based on some results from harmonic analysis and submarkovian operators. As an application we prove the global well-posedness for the two-dimensional Euler-Boussinesq system where the dissipation occurs only on the temperature equation and has the form D=logα(e4+D), with α [0,1/2]. This result improves on an earlier critical dissipation condition .(α = 0) needed for global well-posedness.

Original languageEnglish (US)
Pages (from-to)247-284
Number of pages38
JournalAnalysis and PDE
Volume4
Issue number2
DOIs
StatePublished - 2011

Keywords

  • Boussinesq system
  • Global existence
  • Logarithmic dissipation

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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