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math.AP2025
A geometric characterization of potential Navier-Stokes singularities
Zhen Lei, Xiao Ren, Gang Tian
For a local suitable weak solution to the Navier-Stokes equations, we prove that if the vorticity vectors belong to a double cone in regions of high vorticity magnitude, then the s…
math.AP2015
Global Regularity to the Navier-Stokes Equations for A Class of Large Initial Data
Yukang Chen, Bin Han, Zhen Lei
We prove that for initial data of the form \begin{equation}\nonumber u_0^ε(x) = (v_0^h(x_ε), ε^{-1}v_0^n(x_ε))^T,\quad x_ε= (x_h, εx_n)^T, n \geq 4, \end{equation} the Cauchy probl…