58 citations · 175 across the 13 of their papers we have counts for
13 papers
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…
Stability analysis of the Eulerian-Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension
Yang Yang, Jiajie Chen, Jing-Mei Qiu
In this paper, we construct a novel Eulerian-Lagrangian finite volume (ELFV) method for nonlinear scalar hyperbolic equations in one space dimension. It is well known that the exac…
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…
An Eulerian-Lagrangian Runge-Kutta finite volume (EL-RK-FV) method for solving convection and convection-diffusion equations
Joseph Nakao, Jiajie Chen, Jingmei Qiu
We propose a new Eulerian-Lagrangian Runge-Kutta finite volume method for numerically solving convection and convection-diffusion equations. Eulerian-Lagrangian and semi-Lagrangian…
On the regularity of the De Gregorio model for the 3D Euler equations
Jiajie Chen
We study the regularity of the De Gregorio (DG) model on for initial data with period and in class : is odd and (or $ω_0…
Asymptotically self-similar blowup of the Hou-Luo model for the 3D Euler equations
Jiajie Chen, Thomas Y. Hou, De Huang
Inspired by the numerical evidence of a potential 3D Euler singularity \cite{luo2014potentially,luo2013potentially-2}, we prove finite time singularity from smooth initial data for…
On the Slightly Perturbed De Gregorio Model on
Jiajie Chen
It is conjectured that the generalization of the Constantin-Lax-Majda model (gCLM) due to Okamoto, Sakajo and Wunsch can develop a finite time singularity fr…
Finite time blowup of 2D Boussinesq and 3D Euler equations with velocity and boundary
Jiajie Chen, Thomas Y. Hou
Inspired by the numerical evidence of a potential 3D Euler singularity by Luo-Hou [30,31] and the recent breakthrough by Elgindi [11] on the singularity formation of the 3D Euler e…
Singularity Formation and Global Well-Posedness for the Generalized Constantin-Lax-Majda Equation with Dissipation
Jiajie Chen
We study a generalization due to De Gregorio and Wunsch et.al. of the Constantin-Lax-Majda equation (gCLM) on the real line \[ ω_t + a u ω_x = u_x ω- νΛ^γ ω, \quad u_x = H ω, \] wh…
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…
A Pseudo Knockoff Filter for Correlated Features
Jiajie Chen, Anthony Hou, Thomas Y. Hou
In 2015, Barber and Candes introduced a new variable selection procedure called the knockoff filter to control the false discovery rate (FDR) and prove that this method achieves ex…
A Prototype Knockoff Filter for Group Selection with FDR Control
Jiajie Chen, Anthony Hou, Thomas Y. Hou
In many applications, we need to study a linear regression model that consists of a response variable and a large number of potential explanatory variables and determine which vari…
Validating Sample Average Approximation Solutions with Negatively Dependent Batches
Jiajie Chen, Cong Han Lim, Peter Z. G. Qian +2
Sample-average approximations (SAA) are a practical means of finding approximate solutions of stochastic programming problems involving an extremely large (or infinite) number of s…