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AIMS Mathematics

2017, Volume 2, Issue 3: 451-457. doi: 10.3934/Math.2017.2.451
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Research article

A regularity criterion of weak solutions to the 3D Boussinesq equations

  • 1.
    Department of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia
  • 2.
    Department of Mathematics, University of Mostaganem, Algeria
  • 3.
    Dipartimento di Mathematica e Informatica, Università di Catania, Viale Andrea Doria, 6,95125 Catania, Italy
  • 4.
    RUDN University, 6 Miklukho -Maklay St, Moscow, 117198, Russia
  • Received: 02 June 2017 Accepted: 08 August 2017 Published: 25 August 2017

  • In this note, a regularity criterion of weak solutions to the 3D-Boussinesq equations with respect to Serrin type condition under the framework of Besov space $\dot B_{\infty, \infty.}^r$. It is shown that the weak solution $(u, \theta)$ is regular on $% (0, T] $ if $u$ satisfies $ \int\limits_0^T {\left\| {u( \cdot ,t)} \right\|_{\dot B_{\infty ,\infty .}^r}^{\frac{2}{{1 + r}}}} dt \lt \infty , $ for $ 0 \lt r \lt 1 $. This result improves some previous works.

    Citation: Ahmad Mohammed Alghamdi, Sadek Gala, Maria Alessandra Ragusa. A regularity criterion of weak solutions to the 3D Boussinesq equations[J]. AIMS Mathematics, 2017, 2(3): 451-457. doi: 10.3934/Math.2017.2.451

    Related Papers:

  • In this note, a regularity criterion of weak solutions to the 3D-Boussinesq equations with respect to Serrin type condition under the framework of Besov space $\dot B_{\infty, \infty.}^r$. It is shown that the weak solution $(u, \theta)$ is regular on $% (0, T] $ if $u$ satisfies $ \int\limits_0^T {\left\| {u( \cdot ,t)} \right\|_{\dot B_{\infty ,\infty .}^r}^{\frac{2}{{1 + r}}}} dt \lt \infty , $ for $ 0 \lt r \lt 1 $. This result improves some previous works.


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