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Asymptotic stability of stationary solutions for Hall magnetohydrodynamic equations

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Abstract

In this paper, we consider the large time behavior of the compressible Hall magnetohydrodynamic equations with Coulomb force in \(\mathbb {R}^3\) near the non-constant equilibrium state. We derive the global existence provided that the initial perturbation is sufficiently small. Moreover, under the further assumption that the doping profile is of small variation, we obtain the convergence rates by combining the linear \(L^p\)–\(L^q\) decay estimates.

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Authors and Affiliations

  1. School of Mathematical Sciences Fujian Provincial Key Laboratory on Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, 361005, Fujian, China

    Zhong Tan & Leilei Tong

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  1. Zhong Tan
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  2. Leilei Tong
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Correspondence to Leilei Tong.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant Nos. 11271305, 11531010) and the Fundamental Research Funds for Xiamen University (No. 201412G004).

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Tan, Z., Tong, L. Asymptotic stability of stationary solutions for Hall magnetohydrodynamic equations. Z. Angew. Math. Phys. 69, 51 (2018). https://doi.org/10.1007/s00033-018-0944-7

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  • DOI: https://doi.org/10.1007/s00033-018-0944-7

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