Asymptotic log-Harnack inequality for the 3D stochastic globally modified Allen-Cahn-Navier-Stokes system with degenerate noise Article

Tachim Medjo, T. (2025). Asymptotic log-Harnack inequality for the 3D stochastic globally modified Allen-Cahn-Navier-Stokes system with degenerate noise . JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 547(1), 10.1016/j.jmaa.2025.129293

cited authors

  • Tachim Medjo, T

authors

abstract

  • In this article, we consider a globally modified Allen-Cahn-Navier-Stokes equations in a three dimensional bounded domain and examine some asymptotic behaviors of the strong solution. More precisely, we establish the asymptotic log-Harnack inequality for the transition semigroup associated with the globally modified Allen-Cahn-Navier-Stokes system driven by an additive degenerate noise via the asymptotic coupling method. As consequences of the asymptotic log-Harnack inequality, we derive the gradient estimate, the asymptotic irreducibility, the asymptotic strong Feller property, the asymptotic heat kernel estimate and the ergodicity.

publication date

  • July 1, 2025

published in

Digital Object Identifier (DOI)

volume

  • 547

issue

  • 1