# On a Singular Perturbation of the Navier-Stokes Equations

## TL;DR

This paper analyzes a singular perturbation of the Navier-Stokes equations on compact manifolds, establishing global existence, uniqueness, and convergence of solutions under certain conditions.

## Contribution

It provides new results on the existence, uniqueness, and convergence of solutions for a singularly perturbed Navier-Stokes system on manifolds, including boundary cases.

## Key findings

- Global existence and uniqueness of weak solutions.
- Convergence of regularized solutions to Navier-Stokes solutions.
- Applicability to manifolds with boundary under Dirichlet conditions.

## Abstract

The paper is aimed at analysing a singular perturbation of the Navier-Stokes equations on a compact closed manifold. The case of compact smooth manifolds with boundary under the Dirichlet conditions is also included. Global existence and uniqueness is established for the weak solutions of the Cauchy problem. The solution of the regularised system is shown to converge to the solution of the conventional Navier-Stokes equations provided it is uniformly bounded in parameter.