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Dongxiao Yu

Email: yudx AT math.berkeley.edu

Office:

Starting from 2023 November, I am a math postdoc at University of California, Berkeley, working with Daniel Tataru. My position is for one year.

Previously, I was a math postdoc at Hausdorff Center for Mathematics in Bonn, Germany. My mentor was Herbert Koch.

In 2021 May, I obtained my PhD from University of California, Berkeley. My advisor was Daniel Tataru.

I am currently on the job market. Here is my CV.

Here is a photo of me taken at MFO in Germany.

Research

I am interested in PDE's, especially nonlinear wave and dispersive equations.

Here is a list of my research papers.

  1. Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition. Preprint. arXiv:2407.19416.
  2. (with Herbert Koch) Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms. Preprint. arXiv:2308.07679.
  3. Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Preprint. arXiv:2204.12870.
  4. A uniqueness theorem for 3D semilinear wave equations satisfying the null condition. Pure Appl. Anal. 5 (2023), no. 3, 601–641. arXiv:2109.15041.
  5. Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition. Mem. Amer. Math. Soc. 298 (2024), no.1492. arXiv:2105.11573.
  6. Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition. Comm. Math. Phys. 382 (2021), no. 3, 1961-2013. arXiv:2002.05355.

You can also check arxiv.org/a/yu_d_3.html or Google Scholar for a latest list of my papers.

In addition, I have written a PhD dissertation with title "Modified scattering for a scalar quasilinear wave equation satisfying the weak null condition". This dissertation is a combination of arXiv:2002.05355 and arXiv:2105.11573. Link.

Here is a list of proceedings and reports written by me.

  1. (with Louie Bernhardt and Volker Schlue) John's blow up examples and scattering solutions for semi-linear wave equations. To appear in MATRIX Annals. arXiv:2404.12878.
  2. Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Oberwolfach Rep. 19 (2022), no. 2, 1710 - 1712. Link.

Talks and travel.

Teaching

U Bonn

Instructor for a graduate topic course (V5B8) on quasilinear wave equations in 2022 Summer. Course webpage.

UC Berkeley

Teaching Assistant (Graduate Student Instructor) for undergraduate courses. Duties include teaching discussion sections, holding office hours, grading students’ work, etc.

Teaching Assistant (Graduate Student Instructor) for a graduate course. Duties include holding office hours, grading students’ work, etc.

In 2020 Fall, I was a mentor in the Directed Reading Program. During that semester, I met an undergraduate student weekly and guided him through the textbook on Fourier analysis by Stein and Shakarchi. At the end of this program, my mentee wrote a write-up on the Fourier transform and the wave equation.