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Global Existence and Large Time Behavior of Solutions to 3D MHD System Near Equilibrium

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Abstract

In this paper, we consider the stability problem on perturbation near a physically steady state solution of the 3D generalized incompressible magnetohydrodynamic system in Lei-Lin space. The global stability and analytic estimates for small perturbation are established by the semigroup method in the critical space \(\chi ^{1-2\alpha }(\mathbb {R}^3)\) with \(\frac{1}{2}\le \alpha \le 1\), where linear terms from perturbation incur much difficulty. By introducing a diagonalization process we successfully eliminate the linear terms. Then, by virtue of the analytic estimates for a solution, the temporal decay rate \((1+t)^{-(\frac{5}{4\alpha }-1)}\) of the global solution is obtained.

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Acknowledgements

The research of B Yuan was partially supported by the National Natural Science Foundation of China (No. 11471103).

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  1. School of Mathematics and Information Science, Henan Polytechnic University, Henan, 454000, China

    Yamin Xiao & Baoquan Yuan

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  1. Yamin Xiao
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  2. Baoquan Yuan
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Correspondence to Baoquan Yuan.

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Xiao, Y., Yuan, B. Global Existence and Large Time Behavior of Solutions to 3D MHD System Near Equilibrium. Results Math 76, 73 (2021). https://doi.org/10.1007/s00025-021-01382-w

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