Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

Rui Liang; Yuzhao Wang

doi:10.1007/s00220-024-05116-1

Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

Rui Liang, Yuzhao Wang^*

^*Corresponding author for this work

Mathematics

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Abstract

We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.

Original language	English
Article number	250
Number of pages	69
Journal	Communications in Mathematical Physics
Volume	405
Issue number	10
DOIs	https://doi.org/10.1007/s00220-024-05116-1
Publication status	Published - 1 Oct 2024

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Dynamics of singular stochastic nonlinear dispersive PDEs
Wang, Y. (Principal Investigator)
Engineering & Physical Science Research Council
1/04/21 → 31/03/24
Project: Research Councils

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title = "Gibbs Dynamics for Fractional Nonlinear Schr{\"o}dinger Equations with Weak Dispersion",

abstract = "We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schr{\"o}dinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.",

author = "Rui Liang and Yuzhao Wang",

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doi = "10.1007/s00220-024-05116-1",

language = "English",

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journal = "Communications in Mathematical Physics",

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T1 - Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

AU - Liang, Rui

AU - Wang, Yuzhao

PY - 2024/10/1

Y1 - 2024/10/1

N2 - We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.

AB - We consider the Cauchy problem for the one-dimensional periodic cubic nonlinear fractional Schrödinger equation (FNLS) with initial data distributed via its associated Gibbs measure. We construct global strong solutions with the flow property for the FNLS on the support of the Gibbs measure in the full dispersive range, thus resolving a question proposed by Sun and Tzvetkov (Nonlinear Anal 213, paper no. 112530, 2021). As a byproduct, we prove the invariance of the Gibbs measure and almost sure global well-posedness for FNLS.

U2 - 10.1007/s00220-024-05116-1

DO - 10.1007/s00220-024-05116-1

M3 - Article

SN - 0010-3616

VL - 405

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 10

M1 - 250

ER -

Gibbs Dynamics for Fractional Nonlinear Schrödinger Equations with Weak Dispersion

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Dynamics of singular stochastic nonlinear dispersive PDEs

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