ON THE STOCHASTIC CAHN-HILLIARD-NAVIER-STOKES SYSTEMS WITH SURFACTANT AND JUMP NOISE Article

Tachim Medjo, T. (2026). ON THE STOCHASTIC CAHN-HILLIARD-NAVIER-STOKES SYSTEMS WITH SURFACTANT AND JUMP NOISE . Communications in Mathematical Sciences, 24(6), 1687-1744. 10.4310/CMS.260601221231

cited authors

  • Tachim Medjo, T

authors

abstract

  • We consider the stochastic Cahn-Hilliard-Navier-Stokes system with surfactant on a bounded domain Ω⊂ℝd=2,3, driven by a multiplicative noise of jump type. The system consists of a Navier-Stokes system, coupled with a sixth-order and a fourth–order Cahn–Hilliard equation with singular potential. The existence of a global weak martingale solution is proved. In the two-dimensional case and when the viscosity of the mixture is assumed to be constant, we prove the pathwise uniqueness of the weak solution, and using the Yamada-Watanabe result to derive the existence of a strong probabilistic solution.

publication date

  • January 1, 2026

published in

Digital Object Identifier (DOI)

start page

  • 1687

end page

  • 1744

volume

  • 24

issue

  • 6