ABSTRACT

This paper is dedicated to the study of micropolar fluids which is moving in the presence of a magnetic field in ${\mathbb{R}}^3$. We prove the global existence and uniqueness of strong solutions with initial data $\left({\mathit{u}}_0,{\mathit{w}}_0,{\mathit{b}}_0\right)\in {\mathit{H}}_{\sigma }^1\left({\mathbb{R}}^3\right)\times {\mathit{H}}^1\left({\mathbb{R}}^3\right)\times {\mathit{H}}_{\sigma }^1\left({\mathbb{R}}^3\right)$ satisfying $\begin{array}{rl}& \left(\parallel {\mathit{u}}_0{\parallel }_{{\mathit{L}}^2}^2+\parallel {\mathit{w}}_0{\parallel }_{{\mathit{L}}^2}^2+\parallel {\mathit{b}}_0{\parallel }_{{\mathit{L}}^2}^2\right)\\ & \times \left(\parallel \mathrm{\nabla }{\mathit{u}}_0{\parallel }_{{\mathit{L}}^2}^2+\parallel \mathrm{\nabla }{\mathit{w}}_0{\parallel }_{{\mathit{L}}^2}^2+\parallel \mathrm{\nabla }{\mathit{b}}_0{\parallel }_{{\mathit{L}}^2}^2+\parallel \mathrm{c}\mathrm{u}\mathrm{r}\mathrm{l}{\mathit{u}}_0-2{\mathit{w}}_0{\parallel }_{{\mathit{L}}^2}^2\right)\end{array}$ being small enough.

中文翻译：

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