皮奥特·赫鲁谢尔 , 普斯卡尔·蒙达尔 , 赵博文

Sifan Yu

2026年11月03日 16:30 至 17:30

Tsinghua-Jingzhai-105

Zoom 712 322 9571 (BIMSA)

We present the results on the characteristic initial value problem of the compressible Euler equations in three space dimensions without any symmetry assumption. We allow presence of vorticity and consider any equation of state. Compared to the standard Cauchy problem, where initial data can be freely prescribed on a constant-time hypersurface, we formulate the problem by distinguishing between the "free-component" and the "constrained-component" of the initial data. The latter is to be solved by the "free-component" utilizing the properties of the compressible Euler equations on the initial null hypersurfaces. Then, we establish a priori estimates, followed by a local well-posedness in a neighborhood of initial hypersurfaces. Moreover, we prove a regularity theory in Sobolev norms. Our analysis critically relies on the vectorfield method. This talk is based on the joint works with Jared Speck, Yuxuan Wang and Pin Yu.

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.