Inertial forces in the Navier-Stokes equation

TL;DR

This paper analyzes the inertial force field in the 3D Euler and Navier-Stokes equations, providing estimates based on velocity and gradient magnitudes, with applications to well-posedness issues.

Contribution

It introduces new estimates for inertial forces in the Navier-Stokes equations depending on velocity and gradient norms, aiding in understanding solution behavior.

Findings

Derived bounds for inertial force fields in terms of |u|_∞ and | abla u|_∞

Applied estimates to establish well-posedness results

Enhanced understanding of inertial effects in fluid dynamics equations

Abstract

We estimate the inertial force field in the 3d Euler/Navier-Stokes equation in function of |u|_\infty and |\nabla u |_\infty and provide an application to the well-posed problem