Notes on the blow-up problem of the Euler equations

PDE Seminar
Tuesday, October 27, 2009 - 3:05pm for 1.5 hours (actually 80 minutes)
Skiles 255
Dongho Chae – Sungkyunkwan University, Korea and Universty of Chicago
Zhiwu Lin
We first discuss blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity are considered in various sense. We extend much further, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities. In the second part of the talk we discuss some observations on the Euler equations with symmetries, which shows that the point-wise behavior of the pressure along the flows is closely related to the blow-up of of solutions.