An improved regularity criterion for the 3D magneto-micropolar equations in homogeneous Besov space

Zhang, Panpan; Yuan, Baoquan

doi:10.1016/j.jmaa.2021.125022

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2021

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“…The regularity criterion for the 3D magneto-micropolar fluid equations in Triebel-Lizorkin space was proved in [34]. For more blow-up criteria of smooth solutions and the regularity criteria of weak solutions readers refer to [24,29,30,33]. Recently, Li-Shang [8] and Tan-Wu [20] established the existence of 3D small global smooth solutions in the case of α = β = γ = 1.…”

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confidence: 99%

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

Yuan

Zhang

2021

NZ J Math

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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 $\frac{1}{2}$.

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