Stochastic Navier-Stokes Equations in Unbounded Channel Domains

TL;DR

This paper establishes the existence and uniqueness of strong solutions for stochastic Navier-Stokes equations in unbounded channel domains, advancing mathematical understanding of stochastic fluid dynamics in complex geometries.

Contribution

It introduces a novel approach using local monotonicity and stochastic basic vector fields to prove solvability in unbounded channels.

Findings

Proved existence and uniqueness of solutions.

Developed a new construction method for solvability.

Extended stochastic Navier-Stokes analysis to unbounded domains.

Abstract

In this paper we prove the existence and uniqueness of path-wise strong solution to stochastic viscous flow in unbounded channels with multiple outlets using local monotonicity arguments. We devise a construction for solvability using a stochastic basic vector field.