Stochastic 2-D Navier-Stokes Equation with Artificial Compressibility

TL;DR

This paper investigates the stochastic 2-D Navier-Stokes equation with artificial compressibility, establishing existence, uniqueness, and the transition to incompressible flow using a local monotonicity approach.

Contribution

It provides the first rigorous proof of existence, uniqueness, and the incompressible limit for stochastic Navier-Stokes equations with artificial compressibility.

Findings

Proved existence and uniqueness of strong solutions.

Established the limit to incompressible flow.

Utilized local monotonicity of operators for analysis.

Abstract

In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results are obtained by utilizing a local monotonicity property of the sum of the Stokes operator and the nonlinearity.