On the Cauchy Problem for the Homogeneous Boltzmann-Nordheim Equation for Bosons: Local Existence, Uniqueness and Creation of Moments

被引：21

作者：

Briant, Marc ^{[1
]}

Einav, Amit ^{[2
]}

机构：

[1] Brown Univ, Div Appl Math, 182 George St,Box F, Providence, RI 02192 USA

[2] Univ Cambridge DPMMS, Ctr Math Sci, Wilberforce Rd, Cambridge CB3 0WA, England

来源：

JOURNAL OF STATISTICAL PHYSICS | 2016年 / 163卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Boltzmann-Nordheim equation; Kinetic model for bosons; Bose-Einstein condensation; Subcritical solutions; Local Cauchy problem; BOSE-EINSTEIN PARTICLES; CONDENSATION;

D O I：

10.1007/s10955-016-1517-9

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The Boltzmann-Nordheim equation is a modification of the Boltzmann equation, based on physical considerations, that describes the dynamics of the distribution of particles in a quantum gas composed of bosons or fermions. In this work we investigate the Cauchy theory of the spatially homogeneous Boltzmann-Nordheim equation for bosons, in dimension d >= 3. We show existence and uniqueness locally in time for any initial data in L-infinity (1+vertical bar v vertical bar(s)) with finite mass and energy, for a suitable s, as well as the instantaneous creation of moments of all order.

引用

页码：1108 / 1156

页数：49

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