Speaker：Song Liu (The Hong Kong Polytechnic University)

Time：2024-4-30, 8:30

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

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.