Global well-posedness for the 3D magneto-micropolar equations with fractional dissipation

Abstract

This paper focus on the Cauchy problem of the 3D incompressible magneto-micropolar equations with fractional dissipation in the Sobolev space. Liu, Sun and Xin obtained the global solutions to the 3D magneto-micropolar equations with $\alpha=\beta=\gamma=\frac{5}{4}$. Deng and Shang established the global well-posedness of the 3D magneto-micropolar equations in the case of $\alpha\geq\frac{5}{4}$, $\alpha+\beta\geq\frac{5}{2}$ and $\gamma\geq2-\alpha\geq\frac{3}{4}$. In this paper, we establish the global well-posedness of the 3D magneto-micropolar equations with $\alpha=\beta=\frac{5}{4}$ and $\gamma=\frac{1}{2}$, which improves the results of Liu-Sun-Xin and Deng-Shang by reducing the value of $\gamma$ to $\frac{1}{2}$.

Remarks on the global smooth solution of the 3D generalized magneto‐micropolar equations

“…Jia et al [21] recently investigated the global smooth solution of 3D system with low amount of fractional dissipation. One may also refer to some recent global regularity results of 2D magneto-micropolar equations under different partial dissipation (see [22][23][24][25][26]).…”

Remarks on the global smooth solution of the 3D generalized magneto-micropolar equations

“…Jia, Xie and Dong [9] recently investigated the global smooth solution of 3D system with low amount of fractional dissipation. One may also refer to some recent global regularity results of 2D magneto-micropolar equations under different partial dissipation (see [8,13,19,23,27]).…”