A blow-up criterion of strong solutions to two-dimensional nonhomogeneous micropolar fluid equations with vacuum

Abstract

<p style='text-indent:20px;'>We deal with the Cauchy problem of nonhomogeneous micropolar fluid equations with zero density at infinity in the entire space <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula>. We show that for the initial density allowing vacuum, the strong solution exists globally if a weighted density is bounded from above. It should be noted that our blow-up criterion is independent of micro-rotational velocity.