Geodesic
A regularity criterion to the 3D Boussinesq equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1795-1804

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The paper deals with the regularity criterion for the weak solutions to the 3D Boussinesq equations in terms of the partial derivatives in Besov spaces. It is proved that the weak solution $(u,\theta )$ becomes regular provided that $ (\nabla _{h}u,\nabla _{h}\theta )\in L^{\frac{8}{3}}(0,T;\overset{\cdot }{B} _{\infty ,\infty }^{-1}(\mathbb{R}^{3}))$. Our results improve and extend the well-known results of Fang-Qian [13] for the Navier–Stokes equations.
Keywords: regularity criterion, weak solutions
Mots-clés : Boussinesq equations, Besov space. 
@article{SEMR_2019_16_a107,
     author = {A. M. Alghamdi and I. Ben Omrane and S. Gala and M. A. Ragusa},
     title = {A regularity criterion to the {3D} {Boussinesq} equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1795--1804},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a107/}
}
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A. M. Alghamdi; I. Ben Omrane; S. Gala; M. A. Ragusa. A regularity criterion to the 3D Boussinesq equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1795-1804. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a107/