On the global regularity of $N$-dimensional generalized Boussinesq system

[摘要] 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.

[学科分类] 应用数学

[关键词] Boussinesq system;global regularity;regularity criteria;Besov space