Characteristic Initial Value Problem
for the 3D Compressible Euler Equations
报告专家：余思凡 博士后研究员（新加坡国立大学）
报告时间：6月8日（星期一）16:00-17:00
报告地点：国家天元数学西南中心516
报告摘要：
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.
专家简介：
余思凡，现任新加坡国立大学数学系博士后研究员(合作导师：安歆亮），2023年博士毕业于范德堡大学（博士导师： Jared Speck）。研究方向为偏微分方程，数学物理；在Annals of PDE, Journal of Hyperbolic Differential Equations发表论文。
邀请人：王渝西、李徽
