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

TL;DR

This paper proves the global existence of weak solutions for a complex 3D stochastic ferrohydrodynamic system, combining Navier-Stokes, Maxwell, and magnetization equations with transport noise, extending prior results in related fields.

Contribution

It establishes the existence of weak solutions for a coupled stochastic ferrohydrodynamic system with Bloch-Torrey regularization, generalizing previous work on stochastic MHD and Navier-Stokes equations.

Findings

Proved global existence of weak solutions for the system.

Extended results to include Bloch-Torrey regularization with transport noise.

Utilized Galerkin and compactness methods for proof.

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.