Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons

Toan T. Nguyen; Minh Binh Tran

doi:10.1007/s00205-018-1271-z

Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons

Toan T. Nguyen, Minh Binh Tran

Research output: Contribution to journal › Article

4 Scopus citations

Abstract

In this paper, we consider a quantum Boltzmann equation, which describes the interaction between excited atoms and a condensate. The collision integrals are taken–over energy manifolds, having the full form of the Bogoliubov dispersion law for particle energy. We prove that nonnegative radially symmetric solutions of the quantum Boltzmann equation are bounded from below by a Gaussian distribution, uniformly in time.

Original language	English (US)
Pages (from-to)	63-89
Number of pages	27
Journal	Archive for Rational Mechanics and Analysis
Volume	231
Issue number	1
DOIs	https://doi.org/10.1007/s00205-018-1271-z
State	Published - Jan 22 2019

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All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

Cite this

Nguyen, T. T., & Tran, M. B. (2019). Uniform in Time Lower Bound for Solutions to a Quantum Boltzmann Equation of Bosons. Archive for Rational Mechanics and Analysis, 231(1), 63-89. https://doi.org/10.1007/s00205-018-1271-z

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Access to Document

10.1007/s00205-018-1271-z