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

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.

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