A family of regularity classes for the 3D NSE approximating a critical class Zoran Grujic 35763D Navier-Stokeslocalization of vorticityregularity classes Exploiting the localization of the vortex-stretching mechanism to small spatio-temporal scales obtained in [Zoran Gruji\'c, \textit{Localization and geometric depletion of vortex-stretching in the 3D NSE}, Comm. Math. Phys \textbf{290} (2009), 861--870] and geometric structure of the leading-order vortex-stretching term, a family of regularity classes approximating a critical, NSE-scaling invariant class is obtained. Indiana University Mathematics Journal 2010 text pdf 10.1512/iumj.2010.59.3911 10.1512/iumj.2010.59.3911 en Indiana Univ. Math. J. 59 (2010) 707 - 720 state-of-the-art mathematics http://iumj.org/access/