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

Toan T. Nguyen, Minh Binh Tran

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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 languageEnglish (US)
Pages (from-to)63-89
Number of pages27
JournalArchive for Rational Mechanics and Analysis
Volume231
Issue number1
DOIs
StatePublished - Jan 22 2019

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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