Strong solution of 3D-NSE with exponential damping

TL;DR

This paper proves the existence and uniqueness of strong solutions for a modified 3D incompressible Navier-Stokes equation incorporating exponential damping, advancing mathematical understanding of such damped fluid dynamics models.

Contribution

It introduces a novel exponential damping term into the 3D Navier-Stokes equations and establishes rigorous mathematical results for strong solutions.

Findings

Existence of strong solutions is proven.

Uniqueness of solutions is established.

The damping term influences solution behavior significantly.

Abstract

In this paper we prove the existence and uniqueness of strong solution of the incompressible Navier-Stokes equations with damping $\alpha (e^{\beta|u|^2}-1)u$.