Huang's Seminar on 2024 spring

2024-02-26   Varnothing

This seminar is about the singularity of PDEs in hydrodynamics and quantum mechanics, led by Prof. Huang's group. The relevant informations and sources(including recording videos and documents) will be updated in this post.

Contents

Our seminar proceed as follows: Ni will mainly introduce the recent works by Merle-Raphaël-Rodnianski-Szeftel, which worked out the Millennium problem in compressible version. Some related topics, like shock waves and other types of singularity, will also considered in our seminar. And Meng and Gu will lecture basic theory of elliptic equations. See references at the end.

Schedule and sources

We schedule on every Friday, 2:00-5:30 pm, located at Siyuan building S615, AMSS, CAS.

No. Schedule Topic Lecturer Notes Records Location
1 24.03.08 Singularity & Stability A. Ni written typed offline S615
2 24.03.08 Laplace's equation 1 Y. Gu typed offline S615
3 24.03.15 Smooth implosion 1 A. Ni written offline S615
4 24.03.15 Moser iteration W. Meng typed offline S615
5 24.03.22 Smooth implosion 2 A. Ni written offline S615
6 24.03.22 Spherical blowup 1 Y. Gu written offline S615
7 24.03.29 Smooth implosion 3 A. Ni written offline S615
8 24.03.29 Perron's method W. Meng written offline S615
9 24.04.05 Smooth implosion 4 A. Ni written offline S615
10 24.04.05 Newtonian Potential W. Meng written offline S615
11 24.04.12 Smooth implosion 5 A. Ni written offline S615
12 24.04.12 Iteration method Y. Gu written offline S615
13 24.04.19 Smooth implosion 6 A. Ni written offline S615
13 24.04.19 Laplace equation 4 W. Meng written offline S615
14 24.04.26 Smooth implosion 7 A. Ni written offline S615
15 24.04.26 Hilbert's problem 1 Y. Gu written offline S615
16 24.05.03 Smooth implosion 8 A. Ni written offline S615
17 24.05.10 Smooth implosion 9 A. Ni written offline S615
18 24.05.10 Hilbert's problem 2 Y. Gu written offline S615
19 24.05.17 Smooth implosion 10 A. Ni written offline S615
20 24.05.28 Smooth implosion 11 A. Ni written offline S625
21 24.05.28 Laplace equation 5 Y. Gu written offline S625
22 24.06.04 Smooth implosion 12 A. Ni written offline S625
23 24.06.04 Kazhihov model 1 W. Meng written offline S625
24 24.06.11 Variant viscosity A. Ni written offline S625
25 24.06.11 Kazhihov model 2 W. Meng written offline S625
26 24.06.18 Kazhihov model 3 W. Meng written offline S625
27 24.06.18 Radial blowup Y. Gu written offline S625
28 24.06.25 Kazhihov model 4 W. Meng written offline S625
29 24.06.25 Serrin criterion Y. Gu written online --
30 24.07.09 Kazhihov model 5 W. Meng written offline S625
31 24.07.16 Kazhihov model 6 W. Meng written offline S625
32 24.07.23 Kazhihov model 7 W. Meng written offline S625

References

The main reference for singularity topic includes:

  1. F. Merle, P. Raphaël, I. Rodnianski and J. Szeftel, On the implosion of a three dimensional compressible fluid I: Smooth self-similar inviscid profiles, Ann. of Math. 196 (2022) 2, 567-778.
  2. F. Merle, P. Raphaël, and I. Rodnianski and J. Szeftel, On blow up for the energy super critical defocusing nonlinear Schrödinger equations, Invent. Math. 227 (2022) 1, 247-413.
  3. F. Merle, P. Raphaël, and I. Rodnianski and J. Szeftel, On the implosion of a three dimensional compressible fluid II: Singularity formation, Ann. of Math. 196 (2022) 2, 779-889.

And for the theory of elliptic equations:

  1. D. Gilbarg, N. S. Trudinger, Elliptic partical differential equations of second order, Classics in Mathematics, Vol. 224.
  2. Y. Z. Chen, L. C. Wu, Second order elliptic equations and elliptic systems, Translations of Mathematical Monographs, Vol. 174.