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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.

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  1. Department of Mathematics, Washington State University, Pullman, WA, 99164-3113, USA

    Kazuo Yamazaki

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  1. Kazuo Yamazaki
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Yamazaki, K. On the global regularity of N-dimensional generalized Boussinesq system. Appl Math 60, 109–133 (2015). https://doi.org/10.1007/s10492-015-0087-5

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