On depletion of the vortex-stretching term in the 3D Navier-Stokes equations
This is a very interesting paper concerning the regularity of 3D Navier-Stokes solutions. It is based on an integral representation of the stretching factor of the vorticity evolution, given by \textit{P. Constantin} [SIAM Rev. 36, No. 1, 73--98 (1994; Zbl 0803.35106)]. This result and some new cancellation properties are used for obtaining new properties in the vortex-stretching. A new geometric criteria for preventing finite-time blow-up of N-S solutions is given. An isotropy condition is detected, which can control the evolution of enstrophy. In section 3, a rigorous analysis of enstrophy is given, specifying the control on small and large scales, related with Kolmogorov's theory. Some useful estimates are given in section 4. The main theorem, giving a condition for non-blow-up of vorticity, is proved in the last section.
scientific article; zbMATH DE number 2114616
scientific article