Two-dimensional Riemann problem with four-shock interactions for the Euler equations of potential flow

：刘松（香港理工大学）
：2024-04-30 08:30
：海韵园实验楼105报告厅

报告人：刘松（香港理工大学）

时  间：2024年4月30日8:30

地  点：海韵园实验楼105报告厅

内容摘要:

We present a rigorous approach and related techniques to construct global solutions of the 2-D Riemann problem with four-shock interactions for Euler equations of potential flow. The problem is reformulated to a shock reflection-diffraction problem with respect to a symmetric line, and three critical angles (the vacuum critical angle, the detachment/sonic angles) are introduced to clarify all configurations of the Riemann solutions for the interactions of two-forward and two-backward shocks. Then the problem is further reformulated to the free boundary value problem of a second-order quasilinear equation of mixed elliptic-hyperbolic type in a pseudo-subsonic domain, along with two sonic boundaries varying with the choice of two independent incident angles. The difficulties arise from the degenerate ellipticity near the sonic boundaries, the nonlinearity of the free boundary condition, and the singularity of the solution near the corners of the domain. To solve the problem, we need to analyze the solutions for a quasilinear degenerate elliptic equation by the maximum principle of the mixed-boundary value problem, the theory of the oblique derivative problem, the uniform a priori estimates, and the iteration method. This talk is based on a joint work with Gui-Qiang Chen, Feimin Huang, Alex Cliffe and Qin Wang.  

个人简介：

刘松，香港理工大学博士后。本科毕业于福州大学，博士毕业于中国科学院数学与系统科学研究院，之后在香港城市大学工作一年。刘松的科研兴趣是非线性偏微分方程的理论与应用、双曲守恒律方程组的黎曼问题和可压缩欧拉泊松方程，研究成果发表在Journal of the European Mathematical Society、Nonlinear Analysis: Real World Applications等学术期刊上。

 

联系人：詹伟城