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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear potentials at the fractional scale:sharp regularity
分数尺度 非线性势 尖锐 正则性
2023/11/29
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(I)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Several topics related to nonlinear Schrodinger equation-(II)
非线性 薛定谔方程 量子力学
2023/11/13
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long-time asymptotics of soliton equations via the nonlinear steepest descent method
非线性 最速下降法 孤立子方程 长时间渐近性
2023/11/13
Based on the matrix block technique, the Deift-Zhou nonlinear steepest descent method is developed in order to study the asymptotic analysis of solutions of some nonlinear evolution equations associat...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Transport properties of Gaussian measures for nonlinear Schrodinger equations
非线性 薛定谔方程 高斯测度 输运性质
2023/11/13
In the statistical study of Hamiltonian PDEs out of the equilibrium (lack of invariant measures), it is a natural question to understand the transport properties for canonical Gaussian measures. The f...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：No blow-up by nonlinear It? noise for the Euler equations
非线性 爆炸 欧拉方程 噪声
2023/5/17
We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It? noise with superlinear growth prevents a smooth solution from b...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals
光子晶体 线性非线性特征值问题 近似 计算
2023/5/15
In this talk, we discuss the approximation and computation for the linear and nonlinear eigenvalue problems in photonic crystals. We discretize the shifted Maxwell operator with edge finite elements a...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Normalized solutions of nonlinear Schrodinger equations with exponential critical growth
指数临界增长 非线性薛定谔方程 归一化解
2023/5/15
In this talk, we consider normalized solutions of nonlinear Schrodinger equations in the plane when the nonlinearity satisfies an exponential critical growth. To study the normalized solutions by usin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear Schrodinger equations on metric graphs
度量图 非线性 薛定谔方程
2023/5/12
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Improved error estimates of the splitting methods for the long-time dynamics for the weakly nonlinear Schrodinger equations
弱非线性薛定谔方程 长时间动力学 分裂方法 误差估计
2023/4/21
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nonlinear stability of travelling wave solution of the Navier-Stokes-Poisson system for ions with $\gamma$-law pressure
纳维-斯托克斯-泊松系统 行波解 $γ$定律压力离子 非线性稳定性
2023/4/17
We consider the existence, uniqueness and nonlinear stability of the travelling wave solution of the Navier-Stokes-Poisson system with density-dependent viscosity for ions. Firstly, we derive a system...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 薛定谔方程
2023/4/18
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent results on multi-bubble blow-ups and multi-solitons to stochastic nonlinear Schroinger equations
多气泡膨胀 多孤子 随机非线性 Schroinger equations
2023/4/13
In this talk we review some recent results on the multi-bubble blow-ups and multi-solitons to the focusing stochastic nonlinear Schr鰀inger equations. We will show the corresponding construction and co...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions for a free boundary problem of 3-D compressible Euler equations coupled with a nonlinear Poisson equation
三维 可压缩欧拉方程 耦合 非线性泊松方程 自由边界问题 稳定性条件
2023/4/18
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On nonlinear Schrodinger-type equations with nonlinear damping
非线性阻尼 非线性 薛定谔型方程
2023/4/25
In this talk，I will introduce equations of nonlinear Schrodinger-type augmented by nonlinear damping terms. The nonlinear damping can prevent finite time blow-up in several situations. The solution of...