# FRB

## Seminar

### Plenary Lecture 13: Shock Reflection, von Neumann conjectures, and free boundary problems

Seminar Room 1, Newton Institute

#### Abstract

Co-author: Gui-Qiang Chen (Oxford)We discuss shock reflection problem for compressible gas dynamics, and von Neumann conjectures on transition between regular and Mach reflections. Then we will talk about recent results on existence of regular reflection solutions for potential flow equation up to the detachment angle, and discuss some techniques. The approach is to reduce the shock reflection problem to a free boundary problem for a nonlinear equation of mixed elliptic-hyperbolic type. Open problems will also be discussed.

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