Global existence of strong solutions to the multi-dimensional inhomogeneous incompressible MHD equations

This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when \(\alpha+\beta=1+\frac{n}{2}\) satisfying \(1\leq \beta\leq \alpha\leq\min \{\frac{3\beta}{2},\frac{n}{2}...

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Bibliographic Details
Published inarXiv.org
Main Authors Yuan, Baoquan, Ke, Xueli
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 08.07.2021
Subjects
Cauchy problems
Fluid flow
Magnetohydrodynamic equations
Magnetohydrodynamics
Mathematical analysis
Sobolev space
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Summary:This paper is concerned with the Cauchy problem of the multi-dimensional incompressible magnetohydrodynamic equations with inhomogeneous density and fractional dissipation. It is shown that when \(\alpha+\beta=1+\frac{n}{2}\) satisfying \(1\leq \beta\leq \alpha\leq\min \{\frac{3\beta}{2},\frac{n}{2},1+\frac{n}{4}\}\) and \(\frac{n}{4}<\alpha\) for \(n\geq3\) , then the inhomogeneous incompressible MHD equations has a unique global strong solution for the initial data in Sobolev space which do not need a small condition.
ISSN:2331-8422