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

Zdzislaw Brzezniak; Wei Liu; Jiahui Zhu

doi:10.1016/j.jfa.2021.109021

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

Zdzislaw Brzezniak, Wei Liu, Jiahui Zhu

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	109021
Number of pages	37
Journal	Journal of Functional Analysis
Volume	281
Issue number	4
Early online date	7 Apr 2021
DOIs	https://doi.org/10.1016/j.jfa.2021.109021
Publication status	Published - 15 Aug 2021

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.

Keywords

Lévy noise
Marcus canonical form
Nonlinear Schrödinger equation
Stochastic Strichartz estimate

Access to Document

10.1016/j.jfa.2021.109021

Cite this

@article{0469a653a4eb49e3a0fca89b7ab554f4,

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

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

keywords = "L{\'e}vy noise, Marcus canonical form, Nonlinear Schr{\"o}dinger equation, Stochastic Strichartz estimate",

author = "Zdzislaw Brzezniak and Wei Liu and Jiahui Zhu",

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: {\textcopyright} 2021 Elsevier Inc.",

year = "2021",

month = aug,

day = "15",

doi = "10.1016/j.jfa.2021.109021",

language = "English",

volume = "281",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press",

number = "4",

}

TY - JOUR

T1 - The stochastic Strichartz estimates and stochastic nonlinear Schrödinger equations driven by Lévy noise

AU - Brzezniak, Zdzislaw

AU - Liu, Wei

AU - Zhu, Jiahui

N1 - 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.

PY - 2021/8/15

Y1 - 2021/8/15

N2 - 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.

AB - 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.

KW - Lévy noise

KW - Marcus canonical form

KW - Nonlinear Schrödinger equation

KW - Stochastic Strichartz estimate

UR - http://www.scopus.com/inward/record.url?scp=85104600121&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2021.109021

DO - 10.1016/j.jfa.2021.109021

M3 - Article

AN - SCOPUS:85104600121

SN - 0022-1236

VL - 281

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

M1 - 109021

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Cite this