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.
Accepted author manuscript, 474 KB, PDF document
Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License
Final published version
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Statistical mechanics of the periodic Benjamin Ono equation
AU - Blower, Gordon
AU - Brett, Caroline
AU - Doust, Ian
N1 - 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.
PY - 2019/9/19
Y1 - 2019/9/19
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 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.
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 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.
KW - statistical mechanics
KW - logarithmic Sobolev inequality
KW - solitons
U2 - 10.1063/1.5091737
DO - 10.1063/1.5091737
M3 - Journal article
VL - 60
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
SN - 0022-2488
IS - 9
M1 - 093302
ER -