Connection Between Kinetic Energy And Vorticity Blow-up in 3-D Navier-Stokes Fluid

TL;DR

This paper establishes a mathematical theorem linking the smoothness of kinetic energy and vorticity in 3-D Navier-Stokes fluids, highlighting their interdependence under specific boundary conditions.

Contribution

It introduces a new theorem that directly relates the smoothness of kinetic energy to the smoothness of vorticity in 3-D Navier-Stokes equations.

Findings

A direct relation between kinetic energy and vorticity norm.

Smoothness of kinetic energy implies smoothness of vorticity.

Boundary conditions are crucial for the relation.

Abstract

In this paper the author formulates and proves a theorem that relates smoothness of kinetic energy and smoothness of vorticity in a 3-D Navier-Stokes fluid. Setting velocity and vorticity boundary conditions, a direct relation arises between kinetic energy and the squared Euclidean norm of the vorticity. As a direct result, their smoothness is closely related.