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},1+...
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Main Authors | , |
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Format | Journal Article |
Language | English |
Published |
08.07.2021
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Subjects | |
Online Access | Get full text |
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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. |
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DOI: | 10.48550/arxiv.2107.03654 |