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This article is cited in 3 scientific papers (total in 3 papers)
Differentical equations, dynamical systems and optimal control
A regularity criterion to the 3D Boussinesq equations
A. M. Alghamdia, I. Ben Omraneb, S. Galacd, M. A. Ragusaed a Department of Mathematical Science , Faculty of Applied Science, Umm Alqura University, P.O.B. 14035, Makkah 21955, Saudi Arabia
b Department of Mathematics, Faculty of Science, Imam Mohammad Ibn Saud, Islamic University (IMSIU), P. O. Box 90950, Riyadh, 11623, Saudi Arabia
c Department of Mathematics, Ecole Normale Supérieure de Mostaganem, University of Mostaganem, Box 227, Mostaganem 27000, Algeria
d Dipartimento di Matematica e Informatica, Viale Andrea Doria, 6,
95125-Catania, Italy
e RUDN University, 6, Miklukho - Maklay str., Moscow, 117198, Russia
Abstract:
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:
Boussinesq equations, regularity criterion, weak solutions, Besov space.
Received April 4, 2019, published December 2, 2019
Citation:
A. M. Alghamdi, I. Ben Omrane, S. Gala, M. A. Ragusa, “A regularity criterion to the 3D Boussinesq equations”, Sib. Èlektron. Mat. Izv., 16 (2019), 1795–1804
Linking options:
https://www.mathnet.ru/eng/semr1168 https://www.mathnet.ru/eng/semr/v16/p1795
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