Well posedness of a stochastic hyperviscosity-regularized 3D Navier-Stokes equation

TL;DR

This paper proves the existence and uniqueness of solutions for a stochastic hyperviscosity-regularized 3D Navier-Stokes equation, where the Laplacian is replaced by its a-power with a≥5/4, advancing understanding of regularized fluid models.

Contribution

It establishes well-posedness for a stochastic hyperviscosity-regularized 3D Navier-Stokes equation with a≥5/4, a significant step in analyzing regularized stochastic fluid dynamics models.

Findings

Existence of solutions for a≥5/4

Uniqueness of solutions under the same condition

Extension of well-posedness theory to hyperviscosity-regularized models

Abstract

We analyse the well posedness of a stochastic hyperviscosity-regularized 3D Navier-Stokes equation; this is the Navier-Stokes equation in which the Laplace operator is replaced by its a-power for a>1. We prove existence and uniqueness for this equation assuming a>= 5/4.