A regularity criterion for threedimensional micropolar fluid equations in Besov spaces of negative regular indices
Abstract
In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if \begin{equation*} \int^{T}_{0}\\partial_{3}u\^{\frac{2}{1r}}_{\dot{B}^{r}_{\infty,\infty}} dt<\infty \quad \text{with} \quad 0< r<1, \end{equation*} then, the solutions of the micropolar fluid equations actually are smooth on $(0, T)$. This improves and extends many previous results.
 Publication:

arXiv eprints
 Pub Date:
 May 2020
 DOI:
 10.48550/arXiv.2006.00524
 arXiv:
 arXiv:2006.00524
 Bibcode:
 2020arXiv200600524W
 Keywords:

 Mathematics  Analysis of PDEs