2-D Magneto-Hydrodynamic System with Jump Processes: Well Posedness and Invariant Measures

TL;DR

This paper establishes the well-posedness and existence of invariant measures for a 2-D stochastic magneto-hydrodynamic system influenced by Levy noise, using local monotonicity and stability analysis.

Contribution

It proves the existence and uniqueness of solutions and invariant measures for a 2-D MHD system with Levy noise, advancing stochastic PDE theory.

Findings

Unique strong solutions exist for the system.

Invariant measures are proven to exist and are unique.

Solutions exhibit exponential stability.

Abstract

In this work we prove the existence and uniqueness of the strong solution to the two-dimensional stochastic magneto-hydrodynamic system perturbed by Levy noise. The local monotonicity arguments have been ex- ploited in the proofs. The existence of a unique invariant measures has been proved using the exponential stability of solutions.