Jiajun Tong

5 Yiheyuan Rd
BICMR, Peking University
Haidian District, Beijing 100871
P. R. China

北京市海淀区颐和园路5号
北京大学北京国际数学研究中心
邮编：100871

Office: Jingchunyuan 78, Room 78406-1
办公室：镜春园78号怀新园78406-1室

Email: tongj at bicmr dot pku dot edu dot cn

I am an assistant professor at Beijing International Center for Mathematical Research (BICMR) at Peking University (PKU).

Before joining BICMR, during 2018-2021, I was a Hedrick Assistant Adjunct Professor at the Department of Mathematics, UCLA. My mentor was Prof. Inwon Kim. I got my PhD at New York University in 2018. My advisor was Prof. Fang-Hua Lin.

Here is my full CV.

Research Interests: PDEs and applied analysis, especially evolution free boundary problems, PDEs in fluid dynamics, and calculus of variations.

I am teaching Advanced Mathematics A (I) 《高等数学A（一）》 in Fall 2022.
Click here for the course syllabus. More information will be posted in 北京大学教学网.

I will be teaching Topics in Analysis and PDEs (English) 《分析与方程专题（英文授课）》 in Spring 2023.
The plan is to discuss the elliptic free boundary problems (namely, the obstacle problem), and related topics, such as the Hele-Shaw problem.
More information will be posted in Feb. 2023.

• For postdoc applicants: We have funding for one postdoctoral position starting from 2022. Successful applicant is expected to have expertise in analysis of PDEs in fluid dynamics or related scientific subjects. Apply through Mathjobs and write me an email.
• For PhD applicants: We are looking for PhDs with strong interest and passion about exploring the beauty of math and the world. It would be great if your interests happen to match with mine (see above). Apply through the routine procedure, and in the meantime, write me an email with your transcript and curriculum vitae.
• For PKU undergraduates who are pursuing research opportunities:
  If you are interested in doing undergraduate research on PDEs that arise from physics, fluid dynamics, and biology etc., feel free to contact me. Having learned PDEs is not a prerequisite.
  If you have not yet found a clear interest but would like to see what research in PDE is like (you are not alone!), I am happy to talk too.
  I am on the mentor list of the Applied Math Rotation Program.
  

1. On self-similar finite-time blowups of the De Gregorio model on the real line
   De Huang, Jiajun Tong and Dongyi Wei, arXiv:2209.08232. Submitted.
2. Global solutions to the tangential Peskin problem in 2-D
   Jiajun Tong, arXiv:2205.14723. Submitted.
3. Tumor growth with nutrients: regularity and stability
   Matt Jacobs, Inwon Kim and Jiajun Tong, arXiv:2204.07572. Accepted by Comm. Amer. Math. Soc.
4. Darcy's law with a source term
   Matt Jacobs, Inwon Kim and Jiajun Tong, Arch. Ration. Mech. Anal. 239(3), 1349-1393 (2021).
5. The $L^1$-contraction principle in optimal transport
   Matt Jacobs, Inwon Kim and Jiajun Tong, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. XXIII (4), 1871-1919 (2022).
6. Interface dynamics in a two-phase tumor growth model
   Inwon Kim and Jiajun Tong, Interfaces Free Bound. 23(2):191-304 (2021).
7. Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions
   Zhiyuan Geng and Jiajun Tong, Calc. Var. 59, 57 (2020).
8. Regularized Stokes immersed boundary problems in two dimensions: well-posedness, singular limit, and error estimates
   Jiajun Tong, Comm. Pure Appl. Math. 74(2), pp. 366-449 (2021).
9. Directed migration of microscale swimmers by an array of shaped obstacles: modeling and shape optimization
   Jiajun Tong and Michael J. Shelley, SIAM J. Appl. Math. (2018), 78(5), 2370-2392.
10. On the viscous Camassa-Holm equations with fractional diffusion
    Zaihui Gan, Fang-Hua Lin and Jiajun Tong, Discrete Contin. Dyn. Syst. (2020), 40 (6): 3427-3450.
11. Solvability of the Stokes immersed boundary problem in two dimensions
    Fang-Hua Lin and Jiajun Tong, Comm. Pure Appl. Math. 72(1), pp. 159-226 (2019).
12. Guiding microscale swimmers using teardrop-shaped posts
    Megan S. Davies Wykes, Xiao Zhong, Jiajun Tong, Takuji Adachi, Yanpeng Liu, Leif Ristroph, Michael D. Ward, Michael J. Shelley and Jun Zhang, Soft Matter (2017), 13, pp. 4681-4688.
    (This paper also contributes a cover art to that issue of the journal.)
13. Stability of soft quasicrystals in a coupled-mode Swift-Hohenberg model for three-component systems
    Kai Jiang, Jiajun Tong and Pingwen Zhang, Commun. Comput. Phys. (2016), 19, pp. 559-581.
14. Stability of two-dimensional soft quasicrystals in systems with two length scales
    Kai Jiang, Jiajun Tong, Pingwen Zhang and An-Chang Shi, Phys. Rev. E (2015), 92(4), 042159.

I am co-organizing The Analysis and PDE seminar at BICMR. In Fall 2022, it meets regularly on Tuesdays.
Find more Seminars and Colloquia at BICMR and School of Mathematical Sciences at PKU.