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

Kush Kinra; Manil T. Mohan

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arXiv · 2202.11369

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

Kush Kinra·Manil T. Mohan

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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.

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Kush Kinra, Manil T. Mohan. 2022-02-23. Wong-Zakai approximation and support theorem for 2D and 3D stochastic convective Brinkman-Forchheimer equations. https://arxiv.org/abs/2202.11369

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