2D Backward Stochastic Navier-Stokes Equations with Nonlinear Forcing

TL;DR

This paper establishes the existence and uniqueness of strong solutions for a 2D backward stochastic Navier-Stokes equation with nonlinear forcing, using spectral approximation, truncation, and variational methods.

Contribution

It introduces a novel approach combining spectral, truncation, and variational techniques to analyze backward stochastic Navier-Stokes equations with nonlinear forcing.

Findings

Proves existence and uniqueness of strong solutions.

Develops a new analytical framework for stochastic Navier-Stokes equations.

Bridges deterministic and stochastic analysis in fluid dynamics.

Abstract

The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the truncation and variational techniques. The methodology features an interactive analysis on basis of the regularity of the deterministic Navier-Stokes dynamics and the stochastic properties of the It\^o-type diffusion processes.