The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations

The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Zeitschrift für angewandte Mathematik und Physik Springer Journals

The exponential behavior and stabilizability of the stochastic magnetohydrodynamic equations

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer International Publishing AG, part of Springer Nature
Subject
Engineering; Theoretical and Applied Mechanics; Mathematical Methods in Physics
ISSN
0044-2275
eISSN
1420-9039
D.O.I.
10.1007/s00033-018-0978-x
Publisher site
See Article on Publisher Site

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.

Journal

Zeitschrift für angewandte Mathematik und PhysikSpringer Journals

Published: May 29, 2018

References

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