On boundedness, existence and uniqueness of strong solutions of the Navier-Stokes Equations in 3 dimensions

TL;DR

This paper establishes conditions under which strong solutions to the 3D Navier-Stokes equations exist uniquely and globally, focusing on bounds of vorticity norms without external forces.

Contribution

It provides new criteria for global existence and uniqueness of solutions based on initial vorticity bounds in L_infinity and L_4 norms.

Findings

Derived upper bounds on vorticity norms

Proved global existence under finite initial vorticity norms

Established uniqueness of solutions in specified norm conditions

Abstract

In this paper we consider the Navier-Stokes Equations in 3 dimensions in the vorticity formulation in the absence of the external forces. We derive upper bounds on L_{infinity} norm of omega and use them together with the Local Existence and Uniqueness results to show Global Existence and Uniqueness of the solution provided that at t=0, L_{infinity} norm of omega is finite, or L_4 norm of omega is finite.