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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Blowup of smooth solutions for compressible Navier-Stokes equations
可压缩 Navier-Stokes方程 光滑解 爆破
2023/11/15
In this talk，we discuss the finite time blow up phenomena of smooth solutions to the compressible Navier-Stokes system when the initial data contain vacuums. It is proved that any classical solutions ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On forward/inverse spectral problems, approximation problems and multiple integral formulae for non-smooth solitons
非光滑孤子 正/逆谱问题 近似问题 多重积分公式
2023/4/28
A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable nearly self-similar blowup of the 2D Boussinesq and 3D Euler equations with smooth data
平滑数据 二维布西内斯 三维欧拉方程 稳定近似 自相似爆炸
2023/4/13
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Smooth sonic-supersonic flows in critical nozzles
关键喷嘴 声波-超音速 流动平稳
2023/4/18
Nematic liquid crystals (NLCs) are anisotropic material intermediate that combine the fluidity of liquids with the orientational order of solids. NLCs are best known for their applications in the thri...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Homological instability for the moduli space of smooth 4-manifolds
光滑 4-流形模空间 同调不稳定性
2023/5/5
The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A constructive proof of finite time blowup of 3D incompressible Euler equations with smooth data
光滑数据 三维不可压缩 欧拉方程 有限时间爆破 构造性证明
2023/5/10
Whether the 3D incompressible Euler equations can develop a finite time singularity from smooth initial data is one of the most challenging problems in nonlinear PDEs. In this talk, we will present a ...