Email: dongxiao DOT yu AT vanderbilt DOT edu
Office: B1017, 17th & Horton (Sony Building)
Office Hours (for Fall 2026): 1--3 pm on Mondays, 1--2 pm on Tuesdays, or by appointment.
Address: Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
Photo by Prof. George Bergman, UC Berkeley, November 2023.
Since August 2024, I have been a math postdoc at Vanderbilt University. I am affiliated with the Vanderbilt Initiative for Gravity, Waves, and Fluids. My postdoc mentor is Jared Speck.
From November 2023 to July 2024, I was a postdoc at University of California, Berkeley. From October 2021 to August 2023, I was a postdoc at Hausdorff Center for Mathematics, University of Bonn.
I received my Ph.D. in Mathematics from UC Berkeley in May 2021. My advisor was Daniel Tataru. Before Berkeley, I completed my undergraduate studies at Sun Yat-Sen (Zhongshan) University in Guangzhou, China.
I am on the 2026–27 academic job market for tenure-track assistant professor positions. Here is my Curriculum Vitae.
My research interests lie in partial differential equations, especially nonlinear wave and dispersive equations. My recent work focuses on the long-time dynamics and singularity formation of solutions to these equations, including problems motivated by general relativity and fluid dynamics.
(with Leonardo Abbrescia and Jared Speck) Two global stability theorems for small-data 3D compressible Euler solutions: Unique maximal globally hyperbolic developments with gradient-blowup & smooth global existence in the entire spacetime. Preprint. arXiv:2609.08158.
(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, published version.
(with Herbert Koch) Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms. Comm. Partial Differential Equations 51 (2026), nos. 2–3, 131–192. arXiv:2308.07679, published version.
Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Ann. PDE 11 (2025), no. 2, Paper No. 25. arXiv:2204.12870, published 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, published 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, published 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, published version.
Modified scattering for a scalar quasilinear wave equation satisfying the weak null condition. Link. It combines the results of arXiv:2002.05355 and arXiv:2105.11573.
(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, published version.
Nontrivial global solutions to some quasilinear wave equations in three space dimensions. Oberwolfach Rep. 19 (2022), no. 2, 1710–1712. Link.
See also my arXiv, Google Scholar, and MathSciNet profiles.
Instructor for Math 2400 (Differential Equations with Linear Algebra) in Fall 2026.
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.
Instructor for a graduate topics course (V5B8) on quasilinear wave equations in Summer 2022. Course webpage.
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 the program, my mentee wrote a write-up on the Fourier transform and the wave equation.
Harmonic Analysis and Differential Equations Seminar, UC Berkeley, April 21, 2026. Abstract.
AMS Special Session on Recent Developments in Dynamics of Nonlinear Dispersive Equations, North Dakota State University, April 18, 2026. Abstract.
PDE Seminar, Georgia Institute of Technology, February 17, 2026. Abstract.
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.
Analysis of Partial Differential Equations arising in Physics, Rutgers University, July 13–16, 2026. Website.
AMS Special Session on Recent Developments in Dynamics of Nonlinear Dispersive Equations, North Dakota State University, April 18–19, 2026. Website.
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, Portorož, 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.