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    Rights statement: The final, definitive version of this article has been published in the Journal, Stochastics: An International Journal of Probability and Stochastic Processes, 84 (4), 2012, Informa Plc

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Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

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Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. / Blower, Gordon.
In: Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, Vol. 84, No. 4, 2012, p. 533-542.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Blower, G 2012, 'Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation.', Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, vol. 84, no. 4, pp. 533-542. https://doi.org/10.1080/17442508.2011.597860

APA

Blower, G. (2012). Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports, 84(4), 533-542. https://doi.org/10.1080/17442508.2011.597860

Vancouver

Blower G. Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports. 2012;84(4):533-542. Epub 2011 Sept 29. doi: 10.1080/17442508.2011.597860

Author

Blower, Gordon. / Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation. In: Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports. 2012 ; Vol. 84, No. 4. pp. 533-542.

Bibtex

@article{b0aac183907441ed8ff29dedac77e17c,
title = "Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation.",
abstract = "The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the support of \nu, and \nu is invariant under the KdV flow. This paper shows that \nu satisfies a logarithmic Sobolev inequality. The stationary points of the Hamiltonian on spheres are found in terms of elliptic functions, and they are shown to be linearly stable. The paper also presents logarithmic Sobolev inequalities for the modified period KdV equation and the cubic nonlinear Schrodinger equation for small values of the number operator N.",
keywords = "Gibbs measure, concentration inequality, nonlinear Schrodinger equation",
author = "Gordon Blower",
note = "The final, definitive version of this article has been published in the Journal, Stochastics: An International Journal of Probability and Stochastic Processes, 84 (4), 2012, Informa Plc",
year = "2012",
doi = "10.1080/17442508.2011.597860",
language = "English",
volume = "84",
pages = "533--542",
journal = "Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports",
issn = "1744-2508",
publisher = "Gordon and Breach Science Publishers",
number = "4",

}

RIS

TY - JOUR

T1 - Logarithmic Sobolev inequality for the invariant measure of the periodic Korteweg--de Vries equation.

AU - Blower, Gordon

N1 - The final, definitive version of this article has been published in the Journal, Stochastics: An International Journal of Probability and Stochastic Processes, 84 (4), 2012, Informa Plc

PY - 2012

Y1 - 2012

N2 - The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the support of \nu, and \nu is invariant under the KdV flow. This paper shows that \nu satisfies a logarithmic Sobolev inequality. The stationary points of the Hamiltonian on spheres are found in terms of elliptic functions, and they are shown to be linearly stable. The paper also presents logarithmic Sobolev inequalities for the modified period KdV equation and the cubic nonlinear Schrodinger equation for small values of the number operator N.

AB - The periodic KdV equation arises from a Hamiltonian system with infinite-dimensional phase space L^2(T). Bourgain has shown that there exists a Gibbs measure \nu on balls in the phase space such that the Cauchy problem for KdV is well posed on the support of \nu, and \nu is invariant under the KdV flow. This paper shows that \nu satisfies a logarithmic Sobolev inequality. The stationary points of the Hamiltonian on spheres are found in terms of elliptic functions, and they are shown to be linearly stable. The paper also presents logarithmic Sobolev inequalities for the modified period KdV equation and the cubic nonlinear Schrodinger equation for small values of the number operator N.

KW - Gibbs measure

KW - concentration inequality

KW - nonlinear Schrodinger equation

U2 - 10.1080/17442508.2011.597860

DO - 10.1080/17442508.2011.597860

M3 - Journal article

VL - 84

SP - 533

EP - 542

JO - Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports

JF - Stochastics: An International Journal of Probability and Stochastic Processes formerly Stochastics and Stochastics Reports

SN - 1744-2508

IS - 4

ER -