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Dongxiao Yu

Email: yudx AT math.uni-bonn.de

Office: Endenicher Allee 60 Room 2.005

Address: Mathematisches Institut, Universität Bonn, Endenicher Allee 60, D-53115 Bonn, Germany

Starting from 2021 October, I am a math postdoc at Hausdorff Center for Mathematics, Mathematical Institute, University of Bonn, Germany. My postdoc mentor is Professor Herbert Koch. I am in the Analysis and PDE group.

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

Here is my CV.

Research

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

Here is a list of my papers.

1. (with Herbert Koch) Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms. Preprint. arxiv:2308.07679.
2. Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Preprint. arxiv:2204.12870.
3. A uniqueness theorem for 3D semilinear wave equations satisfying the null condition. To appear in Pure Appl. Anal.. arxiv:2109.15041.
4. Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition. To appear in Mem. Amer. Math. Soc.. arxiv:2105.11573.
5. 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.

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 (with some weaker assumptions) and arxiv:2105.11573. Here is the link to my dissertation.

Teaching

U Bonn

In Summer Semester 2022, I taught V5B8 - Selected Topics in Analysis. The topic of this course is "The vector field method and quasilinear wave equations". Here is the course webpage.

UC Berkeley

I have served as a teaching assistant for several undergraduate math courses (1A, 1B, 53, 55) and for a graduate math course (202B). A complete list of courses which I have taught can be found in my CV.

In 2020 Fall, I was a mentor in the Directed Reading Program.

Here is a photo of me taken at MFO.