Global regularity for a model Navier-Stokes equations on $\Bbb R^3$

TL;DR

This paper proves the global regularity of a modified Navier-Stokes model in three dimensions, demonstrating that solutions remain smooth for all time under certain initial conditions.

Contribution

It introduces a new nonlinear parabolic system closely related to Navier-Stokes and establishes its global regularity for smooth initial data.

Findings

Global regularity for smooth initial data

Model shares scaling and invariance with Navier-Stokes

Solutions remain smooth for all time

Abstract

We study a nonlinear parabolic system for a time dependent solenoidal vector field on $\Bbb R^3$. The nonlinear term of this new model equations is obtained slightly modifying that of the Navier-Stokes equations. The system has the same scaling property and the Galileian invariance as the Navier-Stokes equations. For such system we prove the global regularity for a smooth initial data.