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The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations

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Abstract

This paper studies the two-dimensional stochastic magnetohydrodynamic equations which are used to describe the turbulent flows in magnetohydrodynamics. The exponential behavior and the exponential mean square stability of the weak solutions are proved by the application of energy method. Furthermore, we establish the pathwise exponential stability by using the exponential mean square stability. When the stochastic perturbations satisfy certain additional hypotheses, we can also obtain pathwise exponential stability results without using the mean square stability.

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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, Beijing, 100088, China

    Huaqiao Wang

  2. College of Mathematics and Statistics, Chongqing University, Chongqing, 400044, China

    Huaqiao Wang

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  1. Huaqiao Wang
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Correspondence to Huaqiao Wang.

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Wang, H. The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations. Z. Angew. Math. Phys. 69, 82 (2018). https://doi.org/10.1007/s00033-018-0978-x

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  • DOI: https://doi.org/10.1007/s00033-018-0978-x

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