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## Statistical mechanics of the periodic Benjamin Ono equation

Research output: Working paper

Unpublished

### Standard

Statistical mechanics of the periodic Benjamin Ono equation. / Blower, Gordon; Doust, Ian; Brett, Caroline.

2019.

Research output: Working paper

### Bibtex

@techreport{539461a683234b3ba19450393a6ac239,
title = "Statistical mechanics of the periodic Benjamin Ono equation",
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 parametrized 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 equat",
keywords = "Hamiltonian dynamics, Invariant measures, partial differential equations",
author = "Gordon Blower and Ian Doust and Caroline Brett",
year = "2019",
month = jan
day = "24",
language = "English",
type = "WorkingPaper",

}

### RIS

TY - UNPB

T1 - Statistical mechanics of the periodic Benjamin Ono equation

AU - Blower, Gordon

AU - Doust, Ian

AU - Brett, Caroline

PY - 2019/1/24

Y1 - 2019/1/24

N2 - 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 parametrized 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 equat

AB - 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 parametrized 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 equat

KW - Hamiltonian dynamics

KW - Invariant measures

KW - partial differential equations

M3 - Working paper

BT - Statistical mechanics of the periodic Benjamin Ono equation

ER -