Abstract

This paper gives a further investigation on the regularity criteria for three-dimensional micropolar equations in Besov spaces. More precisely, it is proved that the weak solution $(u, \omega)$ is regular if the velocity $u$ satisfies $$\int_{0}^{T}\| \nabla_{h}u_{h}\|_{\dot{B}_{p,\frac{2p}{3}}^{0}}^{q} d t<\infty,\ with\ \ \frac{3}{p}+\frac{2}{q}=2,\ \frac{3}{2}<p\leq\infty,$$or $$\int_{0}^{T}\| \nabla_{h}u\|_{\dot{B}_{\infty ,\infty}^{-1}}^{\frac{8}{3}} d t<\infty,$$or $$\int_{0}^{T}\|\nabla_{h} u_{h}\|_{\dot{B}_{\infty,\infty}^{-\alpha}}^{\frac{2}{2-\alpha}} d t<\infty,\ with\ 0< \alpha< 1. $$

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.