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