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    Rights statement: Copyright 2019 American Institute of Physics. The following article appeared in Journal of Mathematical Physics 60, 2019 and may be found at http://dx.doi.org/10.1063/1.5091737 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

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Statistical mechanics of the periodic Benjamin Ono equation

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Article number093302
<mark>Journal publication date</mark>19/09/2019
<mark>Journal</mark>Journal of Mathematical Physics
Issue number9
Volume60
Number of pages25
Publication statusPublished
Original languageEnglish

Abstract

The periodic Benjamin--Ono equation is an autonomous Hamiltonian system with a Gibbs measure on $L^2({\mathbb T})$. The paper shows that the Gibbs measures on bounded balls of $L^2$ satisfy some logarithmic Sobolev inequalities. The space of $n$-soliton solutions of the periodic Benjamin--Ono equation, as discovered by Case, is a Hamiltonian system with an invariant Gibbs measure. As $n\rightarrow\infty$, these Gibbs measures exhibit a concentration of measure phenomenon. Case introduced soliton solutions that are parameterised by atomic measures in the complex plane. The limiting distributions of these measures gives the density of a compressible gas that satisfies the isentropic Euler equations.

Bibliographic note

Copyright 2019 American Institute of Physics. The following article appeared in Journal of Mathematical Physics 60, 2019 and may be found at http://dx.doi.org/10.1063/1.5091737 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.