Thursday, June 6, 2024 - 14:30 in V2-210/216
Well-posedness of the three dimensional stochastic Zakharov system
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Martin Spitz from Universität Bielefeld
| Abstract: |
The Zakharov system is a model in plasma physics describing rapid oscillations of the electric field in a conducting plasma. It consists of a Schrödinger and a wave equation with quadratic coupling.
In this talk we show that the stochastic Zakharov system is well-posed in the energy space up to the maximal existence time. The proof intertwines probabilistic techniques such as refined rescaling transforms with dispersive techniques such as the normal form method, Strichartz and local smoothing estimates.
We also present a regularization by noise result which states that finite time blowup before any
given time can be prevented with high probability by adding sufficiently large non-conservative noise.
The talk is based on joint work with Sebastian Herr, Michael Röckner, and Deng Zhang.
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