Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

Multidimensional shock waves and free boundary problems

Gui-Qiang Chen

University of Oxford

In this talk we will analyze several longstanding, fundamental multidimensional shock problems in mathematical fluid mechanics and related free boundary problems for nonlinear partial differential equations of mixed elliptic-hyperbolic type. These shock problems include supersonic flow onto a solid wedge (the Prandtl-Meyer problem), shock reflection-diffraction by a concave cornered wedge (the von Neumann's conjectures), and shock diffraction by a convex cornered wedge (the Lighthill problem). Some recent developments and related mathematical challenges in solving these problems will be discussed. Further trends and open problems in this direction will be also addressed.