Department of Mathematics - Seminar on PDE - Blowup classification for the three-dimensional energy-critical nonlinear heat equation

Advanced mathematical techniques have been developed in the last two decades for rigorous constructions of blowup solutions within the class of finite energy. However, the question of a complete classification of blowup dynamics remains open. In this talk, we consider the energy-critical nonlinear heat equation in R^3 as a model example to illustrate our technique to archive such a blowup classification. It consists of two parts:

1. a review of different techniques for constructing finite-energy blowup solutions, and
2. a rigidity result of the finite-energy blowup.