Abstract:
Shock formation is a physical phenomenon widely observed in the context of continuum mechanics (e.g. fluid dynamics, electromagnetic theory, elasticity...). In this talk, I shall first review some classical and recent results, and then present a geometric perspective on shock formation for a class of quasilinear wave equations, which admits global-in-time solutions with small data. We exhibit a family of smooth initial data leading to breakdown of the smoothness of the solution. Our works combine the ideas from fluid dynamics e.g. shock formation for Euler equations, and the ideas from general relativity e.g. formation of trapped surfaces. This is based on a joint work with Pin Yu.