Wong-Zakai approximation and support theorem for 2D and 3D stochastic convective Brinkman-Forchheimer equations

TL;DR

This paper establishes Wong-Zakai approximation results for 2D and 3D stochastic convective Brinkman-Forchheimer equations driven by Hilbert space valued Wiener noise, and derives the support theorem for their solutions.

Contribution

It proves Wong-Zakai approximation and support theorems for stochastic convective Brinkman-Forchheimer equations, extending existing results to higher dimensions and more complex stochastic systems.

Findings

Wong-Zakai approximation holds for 2D and 3D SCBF equations.

Existence of solutions to approximating systems is established.

Support of the solution distribution is characterized.

Abstract

In this work, we demonstrate the Wong-Zakai approximation results for two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations forced by Hilbert space valued Wiener noise on bounded domains. Even though the existence and uniqueness of a pathwise strong solution to SCBF equations is known, the existence of a unique solution to the approximating system is not immediate from the solvability results of SCBF equations, and we prove it by using Faedo-Galerkin approximation technique and monotonicity arguments. Moreover, as an application of the Wong-Zakai approximation, we obtain the support of the distribution of solutions to SCBF equations.