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Constructing finite time singularities: Non-radial implosion for the compressible Euler, Navier-Stokes and defocusing nonlinear Schrodinger equations
Special Events| Speaker: | Jia Shi, MIT |
| Related Webpage: | https://sites.google.com/view/webpagejia/home?authuser=2 |
| Location: | 1147 MSB |
| Start time: | Thu, Nov 21 2024, 4:30PM |
The compressible Euler and Navier-Stokes equations describe the motion of compressible fluids. The defocusing nonlinear Schrodinger equation is a dispersive equation that has application in many physics areas. Through the Madelung transformation, the defocusing nonlinear Schrodinger 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 Schrodinger 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 Schrodinger 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.