Research Interests
Analysis and Nonlinear Partial Differential Equations, Fluid Dynamics, Singularities and Shock Formation, Free Boundary Problems
Publications and Pre-Prints
A new type of stable shock formation in gas dynamics (with Isaac Neal, Steve Shkoller and Vlad Vicol), Communications on Pure and Applied Analysis, https://doi.org/10.3934/cpaa.2023118, 2023
Global Solutions to the Compressible Euler Equations with Heat Transport by Convection Around Dyson’s Isothermal Affine Solutions, Archive for Rational Mechanics and Analysis, 241(2), 947-1007, http://link.springer.com/article/10.1007/s00205-021-01669-w, 2021
The vacuum boundary problem for the spherically symmetric compressible Euler equations with positive density and unbounded entropy, Journal of Mathematical Physics, 62(2), 021504, https://doi.org/10.1063/5.0037656, 2021
Global existence of the nonisentropic compressible Euler equations with vacuum boundary surrounding a variable entropy state (with Juhi Jang and Mahir Hadžić), Nonlinearity, 34(1), 33-91, https://dx.doi.org/10.1088/1361-6544/abb03b, 2021
Presentations
Vanderbilt University PDE Invited Seminar, January 2024
ICIAM 2023 Contributed Talk, August 2023
AMS 2023 Spring Western Sectional Meeting: Special Session on Nonlinear PDEs in Fluid Dynamics Invited Presentation, May 2023
University of Southern California (USC) PDE Invited Seminar, April 2023
Fluids in New Zealand (FiNZ) Workshop 2023 Contributed Talk (virtual), February 2023
UW-Madison PDE Invited Seminar, December 2022
2022 Shanks Workshop on Mathematical Aspects of Fluid Dynamics Contributed Talk, Vanderbilt University, February 2022
UC Davis PDE and Applied Math Invited Seminar (virtual), May 2021
USC Department of Mathematics Open House Poster Session (virtual), March 2021
MSRI Mathematical problems in fluid dynamics program Five Minute Research Talk (virtual), February 2021
UC Berkeley Harmonic Analysis and Differential Equations Student Seminar (HADES) Invited Talk (virtual), February 2021
UC Davis Student-Run Analysis & PDE Seminar Invited Talk (virtual), February 2021
3rd Annual Meeting of the SIAM Texas-Louisiana Section Analytical Aspect of Nonlinear Wave Equations Mini-symposium Invited Presentation (virtual), October 2020
2020 Shanks Workshop on Mathematical Aspect of Fluids Contributed Talk, Vanderbilt University, March 2020 (canceled)
SIAM Conference on Analysis of Partial Differential Equations Poster Session, Palm Springs, CA, December 2019
MSRI Summer Graduate School Recent topics on well-posedness and stability of incompressible fluid and related topics Research Talk, Berkeley, CA, July 2019
University of Michigan Conference on Nonlinear Partial Differential Equations and Applications Poster Session, July 2019
USC Summer School on Recent Advances in Mathematical Fluid Dynamics Research Talk, May 2019
USC Graduate Analysis Seminar, April 2018
USC Department of Mathematics Graduate Research Poster Session, March 2018