Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

Tadahiro Oh; Nikolay Tzvetkov

doi:10.1007/s00440-016-0748-7

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

Tadahiro Oh, Nikolay Tzvetkov

School of Mathematics

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

Abstract

We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces H^s(핋), s>3/4, are quasi-invariant under the flow.

Original language	English
Pages (from-to)	1121-1168
Number of pages	48
Journal	Probability theory and related fields
Volume	169
Issue number	3-4
Early online date	23 Dec 2016
DOIs	https://doi.org/10.1007/s00440-016-0748-7
Publication status	Published - Dec 2017

Keywords

fourth order nonlinear Schrödinger equation
biharmonic nonlinear Schrödinger equation
Gaussian measure
quasi-invariance

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10.1007/s00440-016-0748-7

OTzPTRFfinalAccepted author manuscript, 554 KB

https://arxiv.org/abs/1508.00824

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

Cite this

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title = "Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schr{\"o}dinger equation",

abstract = "We consider the cubic fourth order nonlinear Schr{\"o}dinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces H^s(핋), s>3/4, are quasi-invariant under the flow. ",

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AU - Tzvetkov, Nikolay

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AB - We consider the cubic fourth order nonlinear Schrödinger equation on the circle. In particular, we prove that the mean-zero Gaussian measures on Sobolev spaces H^s(핋), s>3/4, are quasi-invariant under the flow.

KW - fourth order nonlinear Schrödinger equation

KW - biharmonic nonlinear Schrödinger equation

KW - Gaussian measure

KW - quasi-invariance

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DO - 10.1007/s00440-016-0748-7

M3 - Article

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JO - Probability theory and related fields

JF - Probability theory and related fields

SN - 0178-8051

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ER -

Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation

Abstract

Keywords

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this