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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Laplacian estimates for the cscK equation
cscK方程 拉普拉斯估计 Nash-Moser迭代
2023/11/29
We will report Chen-Cheng’s work on cscK equations. We derive the Laplacian bound using Nash-Moser iteration.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
2023/11/29
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
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：The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/11/13
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： The C0 estimate of the cscK equation
cscK方程 C0估计 ABP最大值原理
2023/12/11
We report the work of Chen-Cheng on the existence of cscK metrics. In this talk I will mainly focus on the C0 estimate, which is derived using the ABP maximum principle.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent progress on steady Prandtl equation and Tollmien-Schlichting waves
稳定 Prandtl方程 Tollmien-Schlichting波
2023/11/9
The Prandtl equation introduced by Prandtl in 1904 is a basic equation describling the behavior of the fluid near the boundary at high Reynolds number regime. In this talk, I will first introduce some...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dean-Kawasaki equation with singular non-local interactions：well-posedness and large deviations
奇异非局部 相互作用 Dean-Kawasaki方程 适定性 大偏差
2023/11/13
The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Harmonic analysis meets wave equation
谐波分析 符合 波动方程
2023/5/10
In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The regularity with respect to domains of the additive eigenvalues of super-quadratic Hamilton-Jacobi equation
超二次 哈密尔顿-雅可比方程 加性特征值域 规律性
2023/4/27
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Long time behavior of the Sine-Gordon equation
正弦 戈登方程 长时间行为 黎曼-希尔伯特问题
2023/4/26
We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted So...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular Solutions to the Yamabe Equation with Prescribed Asymptotics
规定渐近 山部方程 奇异解
2023/4/25
We study positive solutions of the Yamabe equation with isolated singularity and prove the existence of solutions with prescribed asymptotic expansions near singular points and an arbitrarily high ord...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Space-time finite and boundary element methods for the wave equation
波动方程 时空有限元 边界元方法
2023/4/21
In this talk we will review some recent results on space-time finite and boundary element methods for the wave equation. As a first model problem we consider the inhomogeneous wave equation with zero ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/4/13
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...