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arXiv · 2003.07055

Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing

Xuhui Peng·Jianhua Huang·Yan Zheng
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Abstract

We establish the existence, uniqueness and exponential attraction properties of an invariant measure for the MHD equations with degenerate stochastic forcing acting only in the magnetic equation. The central challenge is to establish time asymptotic smoothing properties of the associated Markovian semigroup corresponding to this system. Towards this aim we take full advantage of the characteristics of the advective structure to discover a novel H\"ormander-type condition which only allows for several noises in the magnetic direction.

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Xuhui Peng, Jianhua Huang, Yan Zheng. 2020-03-16. Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing. https://arxiv.org/abs/2003.07055

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