Abstract or Additional Information
In this talk, I will introduce the implosion blow-up results for the compressible Euler, the compressible Navier-Stokes equations, and the defocusing nonlinear Schrödinger equation. We will discuss the existence of self-similar solutions and the stability near those solutions. During the talk, I will mention our work with Gonzalo Cao-Labora, Javier Gómez-Serrano, and Gigliola Staffilani on the first non-radial implosion result for those three equations. I will also mention our work on self-similar solutions of a hydrodynamic equation that may formally arise as potential blow-up profiles of the focusing NLS equation. If there is time, I will also talk about a recent joint work with Kevin Buck, Alvaro Carballeira, and Javier Gómez-Serrano on implosion for the defocusing NLS in dimension 3 and 4.