A global scheme for the incompressible Navier-Stokes equation on compact Riemannian manifolds

TL;DR

This paper introduces a comprehensive scheme for solving the incompressible Navier-Stokes equations on compact Riemannian manifolds, extending classical fluid dynamics models to curved geometric spaces.

Contribution

It presents a novel global scheme specifically designed for the Navier-Stokes equations on compact Riemannian manifolds, bridging fluid dynamics and differential geometry.

Findings

Developed a global solution framework for Navier-Stokes on manifolds

Extended classical models to curved geometric spaces

Provided theoretical foundation for future numerical methods

Abstract

We propose a global scheme for a controlled Navier-Stokes equation system on compact smooth Riemannian manifolds.