Statistical mechanics of the periodic Benjamin Ono equation

Blower, Gordon and Doust, Ian and Brett, Caroline (2019) Statistical mechanics of the periodic Benjamin Ono equation. Working Paper. UNSPECIFIED. (Unpublished)

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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

Item Type:
Monograph (Working Paper)
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
Departments:
ID Code:
130742
Deposited By:
Deposited On:
25 Jan 2019 11:45
Refereed?:
No
Published?:
Unpublished