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

2020/03/16 by Xuhui Peng, Jianhua Huang, Peng, Xuhui +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2003.07055

openalex publication_date 2020/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Hörmander-type condition which only allows for several noises in the magnetic direction.

Citations

• A Coupling Approach¶to Randomly Forced Nonlinear PDE's. I
• Some mathematical questions related to the mhd equations

Cited by

• Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise

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