Friday, January 15, 2021 - 14:15 in ZOOM - Video Conference
Randomized final-state problem for the Zakharov system in dimension three
A talk in the Oberseminar Analysis series by
Martin Spitz
| Abstract: |
The Zakharov system is a model in plasma physics coupling a Schrödinger with a wave equation.
In this talk we study the final-state problem for the Zakharov system in the energy space in three spatial dimensions. We show that after applying a suitable randomization on arbitrary data from the energy space, we almost surely obtain a solution of the nonlinear system scattering to the randomized data. As a corollary, we find that for almost all randomized data below the ground state these scattering solutions are global.
The main difficulty in proving scattering results for the Zakharov system is the slow decay of the wave component. We show that after randomizing the Schrödinger data in physical space and the wave data in the angular variable, we can use time-weighted norms and generalized Strichartz estimates to control the nonlinearities.
Zoom Meeting ID: 955 3980 7363
Passcode: 277200
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