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arXiv · 2001.05259

The Stochastic Strichartz estimates and stochastic nonlinear Schr\"{o}dinger equations driven by L\'{e}vy noise

Zdzisław Brzeźniak·Wei Liu·Jiahui Zhu
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Abstract

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 $L^2(\RR^n)$ with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case.

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Zdzisław Brzeźniak, Wei Liu, Jiahui Zhu. 2020-01-15. The Stochastic Strichartz estimates and stochastic nonlinear Schr\"{o}dinger equations driven by L\'{e}vy noise. https://doi.org/10.1016/j.jfa.2021.109021

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