Dongxiao Yu

Email: dongxiao DOT yu AT vanderbilt DOT edu

Office: B1017, 17th & Horton (Sony Building)

Office Hours: By appointment.

Address: Department of Mathematics, Vanderbilt University, Nashville, TN 37240, US

Photo taken by Prof. George Bergman at UC Berkeley in November 2023.

Starting in August 2024, I am a math postdoc at Vanderbilt University. I am affiliated with the Vanderbilt Initiative for Gravity, Waves, and Fluids. My postdoc mentor is Jared Speck.

Between November 2023 and July 2024, I was a postdoc at University of California, Berkeley. Between October 2021 and August 2023, I was a postdoc at Hausdorff Center for Mathematics, University of Bonn.

I obtained my PhD from UC Berkeley in May 2021. My advisor was Daniel Tataru. Before Berkeley, I did my undergraduate at Sun Yat-Sen (Zhongshan) University in Guangzhou, China.

Here is my CV.

Currently, I am on the job market for tenure-track Assistant Professor positions.

Research

My research interest is in Partial Differential Equations. In particular, I am interested in nonlinear wave and dispersive equations.

Papers

(with Jonathan Luk and Sung-Jin Oh) Late-time tail for a scalar quasilinear wave equation satisfying the weak null condition. Preprint. arXiv:2510.22122.
Timelike asymptotics for global solutions to a scalar quasilinear wave equation satisfying the weak null condition. Forum Math. Sigma 13 (2025), Paper No. e108. arXiv:2407.19416, journal version
(with Herbert Koch) Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms. Preprint. arXiv:2308.07679.
Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Ann. PDE 11 (2025), no. 2, Paper No. 25. arXiv:2204.12870, journal version
A uniqueness theorem for 3D semilinear wave equations satisfying the null condition. Pure Appl. Anal. 5 (2023), no. 3, 601 - 641. arXiv:2109.15041, journal version
Asymptotic completeness for a scalar quasilinear wave equation satisfying the weak null condition. Mem. Amer. Math. Soc. 298 (2024), no.1492. arXiv:2105.11573, journal version
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, journal version

PhD dissertation

Modified scattering for a scalar quasilinear wave equation satisfying the weak null condition. Link. This is a combination of arXiv:2002.05355 and arXiv:2105.11573.

Proceedings and reports

(with Louie Bernhardt and Volker Schlue) John's blow up examples and scattering solutions for semi-linear wave equations. 2023 MATRIX Annals, volume 6 of MATRIX Book Ser., 217 - 232. arXiv:2404.12878, journal version.
Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Oberwolfach Rep. 19 (2022), no. 2, 1710 - 1712. Link.

You are also welcome to check my arXiv page, Google Scholar page, and MathSciNet page.

Teaching

Vanderbilt

Instructor for Math 2410 (Methods of Linear Algebra) in Fall 2025.
Instructor for Math 2400 (Differential Equations with Linear Algebra) in Fall 2024.

Please check Brightspace for course information.

U Bonn

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

UC Berkeley

Teaching Assistant (Graduate Student Instructor) for undergraduate courses. Duties include teaching discussion sections, holding office hours, grading students' work, etc.
- Math 1A (Calculus I): Fall 2016, Fall 2017, Fall 2018
- Math 1B (Calculus II): Spring 2018, Fall 2019
- Math 53 (Multivariable Calculus): Spring 2017
- Math 55 (Discrete Mathematics): Spring 2019

Teaching Assistant (Graduate Student Instructor) for a graduate course. Duties include holding office hours, grading students' work, etc.
- Math 202B (Introduction to Topology and Analysis): Spring 2021

Mentor for the Directed Reading Program: Fall 2020. 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.

Talks and Travel

Talks

Morningside Center of Mathematics, Chinese Academy of Sciences, July 7, 2025. Abstract.
Workshop on Analysis and Related Topics, Institute of Mathematics, AMSS, Chinese Academy of Sciences, July 6, 2025. Abstract.
Beijing Institute of Technology, July 4, 2025. Abstract.
Analysis and PDE Seminar, Beijing International Center for Mathematical Research, Peking University, July 3, 2025. Abstract.
Analysis and PDE Seminar, University of Kentucky, February 11, 2025. Abstract.
(Online) Institute of Mathematics, AMSS, Chinese Academy of Sciences, January 14, 2025. Abstract.
AMS Special Session on Dynamics of Solutions to Wave Equations, University of California, Riverside, October 26, 2024. Abstract.
(Online) Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, October 10, 2024. Abstract.
Analysis and PDE Seminar, UC Berkeley, April 22, 2024. Abstract.
AMS Special Session on Nonlinear Waves, University of Wisconsin-Milwaukee, April 20, 2024. Abstract.
Spring School on Soliton Dynamics, lightning talk, Texas A&M University, March 15, 2024. Abstract.
Harmonic Analysis and Differential Equations Seminar, UC Berkeley, February 13, 2024. Abstract.
Analysis and PDE Seminar, Stanford University, February 6, 2024. Abstract.
Analysis and PDE Seminar, Beijing International Center for Mathematical Research, Peking University, October 16, 2023. Abstract.
Sun Yat-Sen University, October 9, 2023. Abstract.
MATRIX program: Hyperbolic PDEs and Nonlinear Evolution Problems, University of Melbourne, September 21, 2023. Talk on arXiv:2204.12870.
(Online) PDE Seminar, Georgia Institute of Technology, April 11, 2023. Abstract.
(Online) PDE Seminar, Vanderbilt University, October 7, 2022. Abstract.
Summer School 2022: Geometric dispersive PDEs, University Center Obergurgl, September 30, 2022. Talk on arXiv:2204.12870.
Nonlinear PDE Seminar, Karlsruher Institut für Technologie, July 26, 2022. Abstract.
Oberwolfach Workshop: Nonlinear Waves and Dispersive Equations, MFO, June 30, 2022. Talk on arXiv:2204.12870.
(Online) Analysis and PDE Seminar, Beijing International Center for Mathematical Research, Peking University, December 9, 2021. Abstract.
(Online) University of Kentucky, November 3, 2021. Talk on arXiv:2109.15041.
Graduate Seminar on Advanced Topics in PDE, University of Bonn, October 22, 2021. Abstract.
(Online) University of Science and Technology of China, March 15, 2021. Abstract.
(Online) Graduate Student Working Group in MSRI Program “Mathematical problems in fluid dynamics”, MSRI, February 24, 2021. Abstract and video.
(Online) Harmonic Analysis and Differential Equations Seminar, UC Berkeley, October 13, 2020. Abstract.
Harmonic Analysis and Differential Equations Seminar, UC Berkeley, March 12, 2019. Abstract.

Conferences attended (not necessarily a speaker)

Workshop on Analysis and Related Topics, Institute of Mathematics, AMSS, Chinese Academy of Sciences, July 5 - 6, 2025. Website.
Ohio River Analysis Meeting (ORAM 14), University of Cincinnati, March 29 - 30, 2025. Website.
AMS Special Session on Dynamics of Solutions to Wave Equations, University of California, Riverside, October 26 - 27, 2024. Website.
Nonlinear PDEs Summer School, UC Berkeley, June 12 - 14, 2024. Website.
AMS Special Session on Nonlinear Waves, University of Wisconsin-Milwaukee, April 20 - 21, 2024. Website.
Spring School on Soliton Dynamics, Texas A&M, March 14 - 16, 2024. Website.
MATRIX Program: Hyperbolic PDEs and Nonlinear Evolution Problems, MATRIX, Australia, September 18 - 29, 2023. Website.
MSRI Program: Mathematical Problems in Fluid Dynamics, Part 2, MSRI, July 17 - August 11, 2023. Website.
Shocking Developments: New Directions in Compressible and Incompressible Flows, MPI, Germany, June 26 - 30, 2023. Website.
Contemporary Analysis and Its Applications, Portoroz, Slovenia, June 19 - 23, 2023.
Conference: Harmonic Analysis and Partial Differential Equations, HCM, Germany, May 29 - June 2, 2023. Website.
Advances in Nonlinear Analysis and Nonlinear Waves, IHES, France, May 22 - 26, 2023. Website.
Workshop on Analysis and PDEs in Karlsruhe, KIT, Germany, March 27 -31, 2023. Website.
Conference: MathFlows, CIRM, France, December 5 - 9, 2022. Website.
Oberwolfach Seminar: Free Boundary Problems in Fluid Dynamics, MFO, Germany, October 23 - 29, 2022. Website.
Summer School 2022: Geometric Dispersive PDEs, University Center Obergurgl, Austria, September 26 - 30, 2022. Website.
Oberwolfach Workshop: Nonlinear Waves and Dispersive Equations, MFO, Germany, June 26 - July 2, 2022. Website.
(Online, as a Program Associate) MSRI Program: Mathematical Problems in Fluid Dynamics, MSRI, January - May 2021. Website.
(Online) MSRI Virtual Summer Graduate School: Introduction to Water Waves, MSRI, July 27 - August 7, 2020. Website.
Southern California Analysis and PDE Conference, UC San Diego, November 2 - 3, 2019. Website.
Fourth Chicago Summer School in Analysis, University of Chicago, June 18 - 30, 2017. Website.

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