English

Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation

Analysis of PDEs 2025-07-08 v1

Abstract

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.

Keywords

Cite

@article{arxiv.2507.03388,
  title  = {Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation},
  author = {Aristide Ndongmo Ngana and Paul Razafimandimby},
  journal= {arXiv preprint arXiv:2507.03388},
  year   = {2025}
}