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In this talk, I will present our recent result the 2D radially symmetric compressible Navier-Stokes equations with density-dependent viscosity. Under the condition of beta>1, we prove the global exist...
We develop high order discontinuous Galerkin (DG) methods with Lax-Friedrich fluxes for Euler equations under gravitational fields. Such problems may yield steady-state solutions and the density and p...
In this talk, we introduce occupation fields for vertices and oriented edges and compute their distributions. More precisely, under the Markov loop measure, the expected number for crossings of an ori...
Nonlinear potential theory and elliptic regularity theory are two classical topics in the modern analysis of partial differential equations. In this talk I show how these themes merge to solve the lon...
We considers the adaptive stabilization problem for a basic class of linear-quadratic non-cooperative stochastic differential games when the systems matrices are unknown to the regulator and the playe...
In this talk, we will consider the distributed sparse identification problem over wireless sensor networks such that all sensors cooperatively estimate the unknown sparse parameter vector of stochasti...
I will give an introduction to Sobolev extensions, including the use of variants of the Whitney extension technique. I will concentrate on the basics of the theory.
软体机器人是智能机器人领域中的新兴方向,以其可大范围变形、可变材料性质的物理特征和复杂环境适应性强、人机交互安全性高的应用优势而受到广泛关注。基于阻塞效应(jamming transition)的可变刚度性质是软体机器人独有的全新属性,从材料上赋予了机器人“刚柔并济”的能力,不仅能增强机器人适应不同工件或者周围环境的能力,还可应用于人机交互的机器人以提高安全性。和其他软体机器人可变刚度基于阻塞效应...
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
In this talk, we will discuss vacuum static spaces. We firstly introduce the motivation, recent development and some difficult problems that have yet to be solved on vacuum static spaces. Then we pres...
In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...

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