Generalization of 3D-NSE Global Weak Solution with damping

TL;DR

This paper proves the global existence, uniqueness, and continuity of solutions for the incompressible Navier-Stokes equations with a damping term, expanding understanding of their mathematical properties.

Contribution

It establishes the global well-posedness of 3D Navier-Stokes equations with a damping term involving a convex, increasing function.

Findings

Proves global existence of solutions

Shows uniqueness of solutions

Demonstrates continuity in L^2 space

Abstract

In this paper, we prove the global existence, uniqueness and the continuity in $L^2$ of the incompressible Navier-Stokes equations with damping $f(|u|)u$, where $f$ is an increasing, convex and differentiable function on $\mathbb{R}^+$, null at zero.