☆ 4.1 Article

On the global regularity of N-dimensional generalized Boussinesq system

APPLICATIONS OF MATHEMATICS (2015)

Journal

APPLICATIONS OF MATHEMATICS

Volume 60, Issue 2, Pages 109-133

Publisher

ACAD SCIENCES CZECH REPUBLIC, INST MATHEMATICS

DOI: 10.1007/s10492-015-0087-5

Keywords

Boussinesq system; global regularity; regularity criteria; Besov space

Categories

Mathematics, Applied

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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.

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