Journal
APPLICATIONS OF MATHEMATICS
Volume 60, Issue 2, Pages 109-133Publisher
ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS
DOI: 10.1007/s10492-015-0087-5
Keywords
Boussinesq system; global regularity; regularity criteria; Besov space
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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.
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