Weak solutions to the 2D or 3D stochastic NSCHEs

Z. Brzeźniak; A. Ndongmo Ngana

Weak solutions to the 2D or 3D stochastic NSCHEs

Probability 2026-07-11 v1

Authors: Z. Brzeźniak , A. Ndongmo Ngana

Abstract

We consider a diffuse interface model for the mixture of two incompressible fluids driven by transport noise. Under suitable abstract assumptions, we prove the existence of a global weak martingale solution as well as the pathwise uniqueness of a global strong solution in the two dimensional case. This is the first result addressing a unified framework derived from the works by Brze{\'z}niak \& Motyl and Mikulevicius \& Rozovskii, on the study of stochastic partial differential equations.

Keywords

stochastic Navier-Stokes-Cahn-Hilliard equations weak martingale solution pathwise uniqueness transport noise diffuse interface model

Cite

@article{arxiv.2607.10486,
  title  = {Weak solutions to the 2D or 3D stochastic NSCHEs},
  author = {Z. Brzeźniak and A. Ndongmo Ngana},
  journal= {arXiv preprint arXiv:2607.10486},
  year   = {2026}
}