16 citations · 25 across the 6 of their papers we have counts for
7 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…
Quantitative partial regularity of the Navier-Stokes equations and applications
Zhen Lei, Xiao Ren
We prove a logarithmic improvement of the Caffarelli-Kohn-Nirenberg partial regularity theorem for the Navier-Stokes equations. The key idea is to find a quantitative counterpart f…
Radiation of the energy-critical wave equation with compact support
Zhen Lei, Xiao Ren, Zhaojie Yang
We prove exterior energy lower bounds for (nonradial) solutions to the energy-critical nonlinear wave equation in space dimensions , with compactly supported initial…
Existence and uniqueness for plane stationary Navier-Stokes flows with compactly supported force
Julien Guillod, Mikhail Korobkov, Xiao Ren
We study the stationary Navier--Stokes equations in the whole plane with a compactly supported force term and with a prescribed constant spatial limit. Prior to this work, existenc…
Leray's plane stationary solutions at small Reynolds numbers
Mikhail V. Korobkov, Xiao Ren
In the celebrated paper by Jean Leray, published in JMPA journal in 1933, the invading domains method was proposed to construct D-solutions for the stationary Navier-Stokes flow ar…
A Liouville Theorem for Axi-symmetric Navier-Stokes Equations on
Zhen Lei, Xiao Ren, Qi S. Zhang
We establish a Liouville theorem for bounded mild ancient solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb…
On the Constantin-Lax-Majda Model with Convection
Zhen Lei, Jie Liu, Xiao Ren
The well-known Constantin-Lax-Majda (CLM) equation, an important toy model of the 3D Euler equations without convection, can develop finite time singularities [5]. De Gregorio modi…