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The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations. (English) Zbl 1391.35440

Summary: 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.

MSC:

35R60 PDEs with randomness, stochastic partial differential equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35Q35 PDEs in connection with fluid mechanics
76W05 Magnetohydrodynamics and electrohydrodynamics
60H30 Applications of stochastic analysis (to PDEs, etc.)
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