Formation of singularities in nonlinear hyperbolic equations
Abstract
In this talk, I will mostly discuss the singularity formation of Burgers equation. It is well-known that, when the initial data has negative gradient at some point, the solutions blow up in a finite time. We shall study the properties of the blow-up profile of Burgers equation by introducing the self-similar variables and the modulations, which can be used to study the blow-up for general nonlinear hyperbolic systems. If time permits, I will also discuss the singularity formation for the 1D compressible Euler equations and the related open questions.