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The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise

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JournalJournal of Functional Analysis
DateAccepted/In press - 18 Mar 2021
DateE-pub ahead of print - 7 Apr 2021
DatePublished (current) - 15 Aug 2021
Issue number4
Volume281
Number of pages37
Early online date7/04/21
Original languageEnglish

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 Schrödinger 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 Schrödinger equation in L2(Rn) with either focusing or defocusing nonlinearity in the full subcritical range of exponents as in the deterministic case.

Bibliographical note

Funding Information:
This work is supported in part by NSFC ( 12071433 , 11822106 , 11831014 , 12090011 , 11501509 ) and PAPD of Jiangsu Higher Education Institutions.

Publisher Copyright:
© 2021 Elsevier Inc.

    Research areas

  • Lévy noise, Marcus canonical form, Nonlinear Schrödinger equation, Stochastic Strichartz estimate

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