Rough solutions of the relativistic Euler equations
Organizers
Speaker
Sifan Yu
Time
Friday, December 19, 2025 4:30 PM - 5:30 PM
Venue
A3-2-301
Online
Zoom 787 662 9899
(BIMSA)
Abstract
I will discuss recent works on the relativistic Euler equations with dynamic vorticity and entropy. We use a new formulation of the equations, which has geo-analytic structures. In this geometric formulation, we decompose the flow into geometric “sound-wavepart” and “transport-div-curl part.” This allows us to derive sharp results about the dynamics, including the existence of low-regularity solutions. Then, I will discuss the results of rough solutions of the relativistic Euler equations and the role that nonlineargeometric optics play in the framework. Our main result is that the Sobolev norm $H^{2+}$ of the variables in the “wave-part” and the H\”older norm $C^{0,0+}$ of the variables in the “transport-part” can be controlled in terms of initial data for short times.We note that the Sobolev norm assumption $H^{2+}$ is the optimal result for the variables in the “wave-part.” This talk will include the main ideas of the proof, as well as a comparison of the relativistic and non-relativistic scenarios.
Speaker Intro
Sifan Yu is a postdoctoral research fellow at the National University of Singapore, working under the mentorship of Xinliang An. His research focuses on hyperbolic partial differential equations and mathematical physics. He earned his Ph.D. in Mathematicsfrom Vanderbilt University (2023) under the supervision of Jared Speck.