Conditional regularity of solutions of the three-dimensional Navier-Stokes equations and implications for intermittency
Conditional regularity of solutions of the three-dimensional Navier-Stokes equations and implications for intermittency
Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on L2m-norms of the vorticity, denoted by Ωm(t), and particularly on \documentclass[12pt]{minimal}\begin{document}$D_{m} = \big[\varpi_{0}^{-1}\Omega_{m}(t)\big]^{\alpha_{m}}$\end{document}Dm=ϖ0−1Ωm(t)αm, where αm = 2m/(4m − 3) for m ⩾ 1. The first result, more appropriate for the unforced case, …