The stochastic Strichartz estimates and stochastic nonlinear Schr\"{o}dinger equations driven by Lévy noise in the Marcus canonical form

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• Zdzislaw Brzezniak (University of York)
• Wednesday 23 March 2022, 11:30-12:00
• Seminar Room 1, Newton Institute.

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FD2W02 - Fractional kinetics, hydrodynamic limits and fractals

We establish a new version of the stochastic Strichartz estimate for the stochastic convolution driven by jump noise which we apply to the stochastic nonlinear Schr\”{o}dinger equation with nonlinear multiplicative jump noise in the Marcus canonical form.  With the help of the deterministic Strichartz estimates, we prove the existence and uniqueness of a global solution to stochastic nonlinear Schr\”{o}dinger equation in $L^2(\RRn)$ with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case. This talk is based on a joint work with Jiahui Zhu  and W. Liu.

This talk is part of the Isaac Newton Institute Seminar Series series.

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