Global well-posedness of the 3D generalized MHD equations in Lei–Lin–Gevrey and Lei–Lin spaces

Melo, Wilberclay G.; Santos, Thyago Souza Rosa; Zingano, Paulo R.

doi:10.1007/s00033-020-01421-6

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Cited by 5 publications

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“…The global well-posedness of the MHD equations have been investigated extensively and important progress has been made. Readers may refer to [12,13,22,23,25] and the references therein.…”

Section: Introductionmentioning

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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“…The global well-posedness of the MHD equations have been investigated extensively and important progress has been made. Readers may refer to [12,13,22,23,25] and the references therein.…”

Section: Introductionmentioning

confidence: 99%