48 citations · 60 across the 7 of their papers we have counts for
7 papers
A clarification on the distinction between nonlocal error and profile residual error in a computer-assisted proof of 3D Euler singularity
Jiajie Chen, Thomas Y. Hou
In \cite{zhang2025dimension}, the author discusses the applicability of a nonexistence result for self-similar profiles to the Hou--Luo scenario and raises questions about the appr…
Analytic finite-rank corrections for singularly weighted estimates in a computer-assisted proof of 3D Euler singularity
Jiajie Chen, Thomas Y. Hou
Computer-assisted proofs of self-similar singularity formation for fluid equations often rely on numerically constructed approximate profiles. One effective approach to establishin…
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics
Jiajie Chen, Thomas Y. Hou
This is Part II of our paper in which we prove finite time blowup of the 2D Boussinesq and 3D axisymmetric Euler equations with smooth initial data of finite energy and boundary. I…
Potential Singularity of the Axisymmetric Euler Equations with Initial Vorticity for A Large Range of . Part II: the -Dimensional Case
Thomas Y. Hou, Shumao Zhang
In Part II of this sequence to our previous paper for the 3-dimensional Euler equations \cite{zhang2022potential}, we investigate potential singularity of the -diemnsional axisy…
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data I: Analysis
Jiajie Chen, Thomas Y. Hou
Inspired by numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite-time, nearly self-similar blowup of the 2D Boussi…
On stability and instability of singular solutions to the 3D Euler and 2D Boussinesq equations
Jiajie Chen, Thomas Y. Hou
Singularity formation of the 3D incompressible Euler equations is known to be extremely challenging. In [18], Elgindi proved that the 3D axisymmetric Euler equations with no swirl…
On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equation
Jiajie Chen, Thomas Y. Hou, De Huang
We present a novel method of analysis and prove finite time asymptotically self-similar blowup of the De Gregorio model \cite{DG90,DG96} for some smooth initial data on the real li…