5 papers
Finite-Time Blowup for Navier-Stokes with Smooth Forcing, Part I: Construction of Self-Similar Solutions with Admissible Stress and Flat Remainder
Zhen Lei, Xiao Ren
This paper gives a readable and accessible version of the profile-construction part of OpenAI's manuscript "Finite Time Blowup for Navier-Stokes". We regard OpenAI's work as a majo…
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…
Global current-vortex sheets in the two-dimensional ideal incompressible MHD
Yuan Cai, Zhen Lei
The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of cu…
Non-relativistic limit for the cubic nonlinear Klein-Gordon equations
Zhen Lei, Yifei Wu
We investigate the non-relativistic limit of the Cauchy problem for the defocusing cubic nonlinear Klein-Gordon equations whose initial velocity contains a factor of , with $c…
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…