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05/09/2023
Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data II: Rigorous Numerics
This is Part II of our paper in which we prove finite time blowup of the...
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12/22/2022
Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part II: the N-Dimensional Case
In Part II of this sequence to our previous paper for the 3-dimensional ...
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12/22/2022
Potential Singularity of the Axisymmetric Euler Equations with C^α Initial Vorticity for A Large Range of α. Part I: the 3-Dimensional Case
In Part I of our sequence of 2 papers, we provide numerical evidence for...
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07/20/2021
Asymptotic Escape of Spurious Critical Points on the Low-rank Matrix Manifold
We show that the Riemannian gradient descent algorithm on the low-rank m...
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07/14/2021
The nearly singular behavior of the 3D Navier-Stokes equations
Whether the 3D incompressible Navier-Stokes equations can develop a fini...
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07/13/2021
Potential singularity of the 3D Euler equations in the interior domain
Whether the 3D incompressible Euler equations can develop a finite time ...
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05/12/2021
Multiscale Invertible Generative Networks for High-Dimensional Bayesian Inference
We propose a Multiscale Invertible Generative Network (MsIGN) and associ...
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02/12/2021
Potential Singularity Formation of 3D Axisymmetric Navier-Stokes Equations with Degenerate Variable Diffusion Coefficients
In this paper, we present strong numerical evidences that the 3D axisymm...
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12/31/2020
Fast Global Convergence for Low-rank Matrix Recovery via Riemannian Gradient Descent with Random Initialization
In this paper, we propose a new global analysis framework for a class of...
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11/28/2019
Analysis of Asymptotic Escape of Strict Saddle Sets in Manifold Optimization
In this paper, we provide some analysis on the asymptotic escape of stri...
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09/10/2019
A class of robust numerical methods for solving dynamical systems with multiple time scales
In this paper, we develop a class of robust numerical methods for solvin...
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04/10/2018