Global regularity for a model Navier-Stokes equations on ${\mathbb{R}}^3$

Abstract

We study a nonlinear parabolic system for a time dependent solenoidal vector field on ${\mathbb{R}}^3$. 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.

9 pages(to appear in Analysis)