Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913926723141632 |
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| author | Ngana, Aristide Ndongmo Razafimandimby, Paul |
| author_facet | Ngana, Aristide Ndongmo Razafimandimby, Paul |
| contents | In this article, we consider a stochastic ferrohydrodynamic system which describes the Bloch-Torrey regularization of the motion of an electrically conducting ferrofluids driven by transport noise filling a 3D bounded domain with a smooth boundary. We prove the global existence of a probabilistic weak solution of the stochastic system by making use of the combination of Galerkin method and compactness method. The system under study is basically a coupling of the Navier-Stokes equations with internal rotation, the Maxwell equations and the ferromagnetization equations. Thus, our result can be seen as a modest generalization of the existing results on the global existence of weak solutions of stochastic Magnetohydrodynamic (MHD), Navier-Stokes and Bloch type equations on 3D bounded domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03388 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation Ngana, Aristide Ndongmo Razafimandimby, Paul Analysis of PDEs In this article, we consider a stochastic ferrohydrodynamic system which describes the Bloch-Torrey regularization of the motion of an electrically conducting ferrofluids driven by transport noise filling a 3D bounded domain with a smooth boundary. We prove the global existence of a probabilistic weak solution of the stochastic system by making use of the combination of Galerkin method and compactness method. The system under study is basically a coupling of the Navier-Stokes equations with internal rotation, the Maxwell equations and the ferromagnetization equations. Thus, our result can be seen as a modest generalization of the existing results on the global existence of weak solutions of stochastic Magnetohydrodynamic (MHD), Navier-Stokes and Bloch type equations on 3D bounded domain. |
| title | Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.03388 |