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Existence of weak solution of 3D ferrohydrodynamic equations with transport noise: Bloch-Torrey regularisation
Aristide Ndongmo Ngana, Paul Razafimandimby
https://arxiv.org/abs/2507.03388

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

A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference
Manuel Gonz\'alez-Navarrete
https://arxiv.org/abs/2506.18313

A stochastic model for the diffusion of competing opinions with trend-following, opposition, and indifference
We study a stochastic model for the diffusion of competing opinions in a population composed of three types of agents: trend-followers, opposers, and indifferent individuals. The decision dynamics are driven by reinforcement mechanisms, modulated by a latent trend process, allowing us to capture realistic features such as amplification, resistance, and randomness in opinion formation. We derive explicit formulas for the finite-time moments of the opinion count vector and establish a set of stro…

Averaged models for compressible two-phase stratified flows on thin domains
Nicolas Seguin (ANGUS), Khaled Saleh (I2M, AMU), Pierrick Le Vourc'H (ANGUS)
https://arxiv.org/abs/2506.08542

Averaged models for compressible two-phase stratified flows on thin domains
This paper deals with the derivation of compressible two-phase flow models. We use a thin domain approximation of a two-layer configuration governed by the Navier-Stokes equations, following the works [H. B. Stewart and B. Wendroff, J. Comp. Phys., 56 (1984)] and [V. H. Ransom and D. L. Hicks, J. Comput. Phys., 75 (1988)]. In order to recover source terms and two-velocity models directly from this asymptotic analysis, we remove the continuity of the tangential component of the velocity at the i…