Large deviation for a 2D Allen–Cahn–Navier–Stokes model under random influences

Article type: Research Article

Authors: Deugoué, G.^a | Tachim Medjo, T.^{a; b; *}

Affiliations: [a] Department of Mathematics and Computer Science, University of Dschang, P.O. BOX 67, Dschang, Cameroon | [b] Department of Mathematics, Florida International University, DM413B University Park, Miami, Florida 33199, USA

Correspondence: [*] Corresponding author. E-mail: tachimt@fiu.edu.

Abstract: In this article, we derive a large deviation principle for a 2D Allen–Cahn–Navier–Stokes model under random influences. The model consists of the Navier–Stokes equations for the velocity, coupled with an Allen–Cahn equation for the order (phase) parameter. The proof relies on the weak convergence method that was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 47 (2011) 725–747) and based on a variational representation on infinite-dimensional Brownian motion.

Keywords: Allen–Cahn, Navier–Stokes, strong solutions, Gaussian noise, large deviations

DOI: 10.3233/ASY-201625

Journal: Asymptotic Analysis, vol. 123, no. 1-2, pp. 41-78, 2021