- Series
- Job Candidate Talk
- Time
- Tuesday, December 3, 2024 - 11:00am for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jia Shi – MIT – jiashi@mit.edu – https://sites.google.com/view/webpagejia/home?authuser=2
- Organizer
- Gong Chen
The compressible Euler and Navier-Stokes equations describe the motion of compressible fluids. The defocusing nonlinear Schr\"odinger equation is a dispersive equation that has application in many physics areas. Through the Madelung transformation, the defocusing nonlinear Schr\"odinger equation is connected with the compressible Euler equation. In this colloquium I will start from the compressible Euler/Navier-Stokes equation and introduce the blow-up result called implosion. Then I will introduce the defocusing nonlinear Schr\"odinger equation and the longstanding open problem on the blow-up of its solutions in the energy supercritical regime. In the end I will talk about the Madelung transformation and its application to transfer the implosion from the compressible Euler to the defocusing nonlinear Schr\"odinger equation. 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.