Stochastic Logarithmic Schrödinger Equations: Energy Regularized Approach

Jianbo Cui; Liying Sun

doi:10.1137/21M1442425

Stochastic Logarithmic Schrödinger Equations: Energy Regularized Approach

Jianbo Cui, Liying Sun

Research output: Journal article publication › Journal article › Academic research › peer-review

2 Citations (Scopus)

Abstract

In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (SlogS) equation driven by either additive noise or multiplicative noise. The key ingredient lies in the regularized SlogS (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of the RSlogS equations. In addition, temporal Holder regularity estimates and uniform estimates in energy space H1(\scrO ) and weighted Sobolev space L2 \alpha (\scrO ) of the solutions for both the SlogS equation and RSlogS equation are also obtained.

Original language	English
Pages (from-to)	3044-3080
Number of pages	37
Journal	SIAM Journal on Mathematical Analysis
Volume	55
Issue number	4
DOIs	https://doi.org/10.1137/21M1442425
Publication status	Published - Aug 2023

Keywords

energy regularized approximation
logarithmic nonlinearity
stochastic Schrodinger equation
strong convergence

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

More information

10.1137/21M1442425

http://hdl.handle.net/10397/100034

Cite this

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title = "Stochastic Logarithmic Schr{\"o}dinger Equations: Energy Regularized Approach",

abstract = "In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (SlogS) equation driven by either additive noise or multiplicative noise. The key ingredient lies in the regularized SlogS (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of the RSlogS equations. In addition, temporal Holder regularity estimates and uniform estimates in energy space H1(\scrO ) and weighted Sobolev space L2 \alpha (\scrO ) of the solutions for both the SlogS equation and RSlogS equation are also obtained.",

keywords = "energy regularized approximation, logarithmic nonlinearity, stochastic Schrodinger equation, strong convergence",

author = "Jianbo Cui and Liying Sun",

year = "2023",

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doi = "10.1137/21M1442425",

language = "English",

volume = "55",

pages = "3044--3080",

journal = "SIAM Journal on Mathematical Analysis",

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T1 - Stochastic Logarithmic Schrödinger Equations: Energy Regularized Approach

AU - Cui, Jianbo

AU - Sun, Liying

PY - 2023/8

Y1 - 2023/8

N2 - In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (SlogS) equation driven by either additive noise or multiplicative noise. The key ingredient lies in the regularized SlogS (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of the RSlogS equations. In addition, temporal Holder regularity estimates and uniform estimates in energy space H1(\scrO ) and weighted Sobolev space L2 \alpha (\scrO ) of the solutions for both the SlogS equation and RSlogS equation are also obtained.

AB - In this paper, we prove the global existence and uniqueness of the solution of the stochastic logarithmic Schrodinger (SlogS) equation driven by either additive noise or multiplicative noise. The key ingredient lies in the regularized SlogS (RSlogS) equation with regularized energy and the strong convergence analysis of the solutions of the RSlogS equations. In addition, temporal Holder regularity estimates and uniform estimates in energy space H1(\scrO ) and weighted Sobolev space L2 \alpha (\scrO ) of the solutions for both the SlogS equation and RSlogS equation are also obtained.

KW - energy regularized approximation

KW - logarithmic nonlinearity

KW - stochastic Schrodinger equation

KW - strong convergence

UR - http://www.scopus.com/inward/record.url?scp=85171577658&partnerID=8YFLogxK

U2 - 10.1137/21M1442425

DO - 10.1137/21M1442425

M3 - Journal article

AN - SCOPUS:85171577658

SN - 0036-1410

VL - 55

SP - 3044

EP - 3080

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Stochastic Logarithmic Schrödinger Equations: Energy Regularized Approach

Abstract

Keywords

ASJC Scopus subject areas

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