Geodesic
On the global regularity of $N$-dimensional generalized Boussinesq system
Applications of Mathematics, Tome 60 (2015) no. 2, pp. 109-133.

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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.
DOI : 10.1007/s10492-015-0087-5
Classification : 35B65, 35Q30, 35Q35, 35Q86, 76D03
Keywords: Boussinesq system; global regularity; regularity criteria; Besov space 
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     title = {On the global regularity of $N$-dimensional generalized {Boussinesq} system},
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Yamazaki, Kazuo. On the global regularity of $N$-dimensional generalized Boussinesq system. Applications of Mathematics, Tome 60 (2015) no. 2, pp. 109-133. doi : 10.1007/s10492-015-0087-5. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0087-5/

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