On the global regularity of N-dimensional generalized Boussinesq system

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Abstract

We study the N-dimensional Boussinesq system with dissipation and diffusion generalized in terms of fractional Laplacians. In particular, we show that given the critical dissipation, a solution pair remains smooth for all time even with zero diffusivity. In the supercritical case, we obtain component reduction results of regularity criteria and smallness conditions for the global regularity in dimensions two and three.

Original languageEnglish
Pages (from-to)109-133
Number of pages25
JournalApplications of Mathematics
Volume60
Issue number2
DOIs
StatePublished - 2015

Keywords

  • Besov space
  • Boussinesq system
  • global regularity
  • regularity criteria

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