A note on the regularity criterion of weak solutions for the micropolar fluid equations

Authors

  • Berrabah Bendoukha University of Mostaganem
  • Sadek Gala ENS of Mostaganem
  • Maria Alessandra Ragusa Universita di Catania

Keywords:

micropolar fluid equations, weak solutions, regularity criteria

Abstract

The aim of this paper is to investigate the regularity criterion of
Leray-Hopf weak solutions to the 3D incompressible micropolar fluid
equations. It is shown that if
\begin{equation*}
\int_{0}^{T}\frac{\left\Vert \nabla \pi (t)\right\Vert _{L^{r}}^{\frac{2r}{3(r-1)}}}{\left\Vert u(\cdot ,t)\right\Vert _{L^{3}}^{\alpha }+\left\Vert
\omega (\cdot ,t)\right\Vert _{L^{3}}^{\alpha }}dt<\infty \text{ \ \ with \ }
\alpha =\left\{
\begin{array}{c}
3,\text{ \ \ }1<r\leq \frac{9}{7}, \\
\frac{2r}{3(r-1)},\text{ \ \ }\frac{9}{7}<r<3,
\end{array}
\right.
\end{equation*}
then the corresponding weak solution $(u,\omega )$ is regular on $[0,T]$,
which is an obvious extension of the previous results.

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Author Biographies

Berrabah Bendoukha, University of Mostaganem

Department of Mathematics & Informatics,
University of Mostaganem,
Box 227, Mostaganem 27000,
Algeria

Sadek Gala, ENS of Mostaganem

First address:
Department of Sciences Exactes,
ENS of Mostaganem,
Box 227, Mostaganem 27000,
Algeria


Second address:
Dipartimento di Matematica e Informatica,
Universit\`{a} di Catania,
Viale Andrea Doria,
6 95125 Catania,
Italy

Maria Alessandra Ragusa, Universita di Catania

First address:
Dipartimento di Matematica e Informatica,
Universit\`{a} di Catania,
Viale Andrea Doria,
6 95125 Catania,
Italy


Second address:
Rudin University,
6 Miklukho Maklay St,
Moscow, 117198, Russia

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Published

04-02-2021

How to Cite

Bendoukha, B., Gala, S., & Ragusa, M. A. (2021). A note on the regularity criterion of weak solutions for the micropolar fluid equations. New Zealand Journal of Mathematics, 50, 101–108. Retrieved from https://nzjmath.org/index.php/NZJMATH/article/view/78

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