Wednesday, January 10, 2024 - 16:00 in U2-232
Type II blow up dynamics in finite-time for the 3D quintic NLS and 4D Zakharov system
A talk in the Oberseminar Analysis series by
Tobias Schmid from Lausanne
| Abstract: |
In this talk we present results on finite time renormalization (or concentration) blow up near the ground state soliton for the 3D energy-critical nonlinear Schrödinger and the 4D Zakharov equation. We first outline the construction of „well behaved“ approximate solutions near the respective bulk solutions with a fast decaying error. While the constructions have a common heurist approach motivated from matched asymptotic expansions, the latter equation requires a more intricate analysis of the occuring error functions due to the coupled wave interaction. In the second part, we explain how to perturbatively obtain exact solutions using Fourier techniques for the linearized flow. In particular, we discuss novel difficulties compared to previous results in same direction.
Within the CRC this talk is associated to the project(s): A1 |
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