Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909597677125632 |
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| author | Wang, Xue Zhang, Jiangwei Huang, Jianhua |
| author_facet | Wang, Xue Zhang, Jiangwei Huang, Jianhua |
| contents | This paper is concerned with the ergodicity for stochastic 2D fractional magneto-hydrodynamic equations on the two-dimensional torus driven by a highly degenerate pure jump Lévy noise. We focus on the challenging case where the noise acts in as few as four directions, establishing new results for such high degeneracy. We first employ Malliavin calculus and anticipative stochastic calculus to demonstrate the equi-continuity of the semigroup (or so-called the e-property), and then verify the weak irreducibility of the solution process. Therefore, the uniqueness of invariant measure is proven. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_21350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise Wang, Xue Zhang, Jiangwei Huang, Jianhua Probability Analysis of PDEs This paper is concerned with the ergodicity for stochastic 2D fractional magneto-hydrodynamic equations on the two-dimensional torus driven by a highly degenerate pure jump Lévy noise. We focus on the challenging case where the noise acts in as few as four directions, establishing new results for such high degeneracy. We first employ Malliavin calculus and anticipative stochastic calculus to demonstrate the equi-continuity of the semigroup (or so-called the e-property), and then verify the weak irreducibility of the solution process. Therefore, the uniqueness of invariant measure is proven. |
| title | Ergodicity for the fractional Magneto-Hydrodynamic equations driven by a degenerate pure jump noise |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2504.21350 |