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 PhD advisor was Prof. Fang-Hua Lin.

Here is my full CV.

Research Interests: PDEs and applied analysis. More precisely:

• Fluid-structure interaction problems: the immersed boundary problem (aka. Peskin problem);
• PDEs in fluid dynamics: the incompressible Euler equation and related fluid models, especially their steady-state solutions, traveling-wave solutions, and blow-ups;
• Evolution free boundary problems: free boundary problems in tumor growth models, Muskat problem, Hele-Shaw problem, etc.;
• Calculus of variations: liquid crystal models, minimizing movement scheme.

I will be teaching Mathematical Analysis (I) 《数学分析 (I)》 in Fall 2025.
课程大纲将在九月初发布，更多信息将发布在北京大学教学网。

1. Steady contiguous vortex-patch dipole solutions of the 2D incompressible Euler equation
   De Huang and Jiajun Tong, arXiv:2406.09849. Accepted by Arch. Ration. Mech. Anal.
2. Convergence of free boundaries in the incompressible limit of tumor growth models
   Jiajun Tong and Yuming Paul Zhang, J. Math. Pures Appl. (9). 203, 103752 (2025).
3. Geometric properties of the 2-D Peskin problem
   Jiajun Tong and Dongyi Wei, Ann. PDE. 10, 24 (2024).
4. On self-similar finite-time blowups of the De Gregorio model on the real line
   De Huang, Jiajun Tong and Dongyi Wei, Comm. Math. Phys. 402, 2791-2829 (2023).
5. Global solutions to the tangential Peskin problem in 2-D
   Jiajun Tong, Nonlinearity (2024), 37(1), 015006.
6. Tumor growth with nutrients: regularity and stability
   Matt Jacobs, Inwon Kim and Jiajun Tong, Comm. Amer. Math. Soc. 3 (2023), 166-208.
7. Darcy's law with a source term
   Matt Jacobs, Inwon Kim and Jiajun Tong, Arch. Ration. Mech. Anal. 239(3), 1349-1393 (2021).
8. 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).
9. Interface dynamics in a two-phase tumor growth model
   Inwon Kim and Jiajun Tong, Interfaces Free Bound. 23(2):191-304 (2021).
10. Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions
    Zhiyuan Geng and Jiajun Tong, Calc. Var. 59, 57 (2020).
11. 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).
12. 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.
13. 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.
14. 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).
15. 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 contributed a cover art to that issue of the journal.)
16. 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.
17. 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.

欢迎申请我的博士后、博士研究生、以及本科生科研！
Postdocs, PhDs, and undergraduate research applicants are wanted!

• To postdoc applicants: We have funding for one postdoctoral position. Successful applicant is expected to have expertise in rigorous analysis of free boundary problems, and/or PDEs in fluid dynamics or related scientific subjects. Apply through Mathjobs and write me an email.
• To 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.
• 给想做本研的北大同学们：如果你对偏微分方程感兴趣（尤其是物理、流体力学、生物等领域的方程），欢迎联系我做本研。如果你已经接触过偏微分方程，那会十分有帮助，但那并不是开始本研的必要条件。
  如果你还没有确定自己的兴趣，但想先了解一下偏微分方程（不少同学大概都与你有类似的想法），也欢迎与我交流。
  
• 如果你需要我写推荐信：无论是什么类型的推荐信（申请奖学金、国内外的研究生项目、暑期学校、科研项目等等），请确保我比较熟悉你的情况。我会自己撰写，据实推荐。

BICMR and the School of Mathematical Sciences at PKU hold The Analysis and PDE seminar jointly. In Spring 2025, it meets on Monday afternoons.
Find more Seminars and Colloquia at BICMR and School of Mathematical Sciences at PKU.