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 α+β=1+n2 satisfying 1≤β≤α≤min{3β2,n2,1+n4} and max{n4,n+16}<α for n≥3, the inhomogeneous incompressibl...

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Bibliographic Details
Published inApplied mathematics and computation Vol. 427; p. 127154
Main Authors Yuan, Baoquan, Ke, Xueli
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.08.2022
Subjects
Global strong solution
Inhomogeneous
Magnetohydrodynamic equations
Magnetohydrodynamic equations
35B65
Inhomogeneous
35Q35
Global strong solution
76N10
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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 α+β=1+n2 satisfying 1≤β≤α≤min{3β2,n2,1+n4} and max{n4,n+16}<α for n≥3, the inhomogeneous incompressible MHD equations have a unique global strong solution for the initial data in some Sobolev spaces without requiring small conditions.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2022.127154