Acoustic limit for the Boltzmann equation in the whole space

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)7-19
Journal / PublicationJournal of Mathematical Analysis and Applications
Volume367
Issue number1
Publication statusPublished - 1 Jul 2010
Externally publishedYes

Abstract

This paper is devoted to the following rescaled Boltzmann equation in the acoustic time scaling in the whole space(0.1)∂t Fε{lunate} + v ṡ ∇x Fε{lunate} = frac(1, ε{lunate}) Q (Fε{lunate}, Fε{lunate}), x ∈ R3, t > 0, with prescribed initial dataFε{lunate} |t = 0 = Fε{lunate} (0, x, v), x ∈ R3 . For a solutionFε{lunate} (t, x, v) = μ + sqrt(μ) ε{lunate} fε{lunate} (t, x, v) to the rescaled Boltzmann equation (0.1) in the whole space R3 for all t ≥ 0 with initial dataFε{lunate} (0, x, v) = F0ε{lunate} (x, v) = μ + sqrt(μ) ε{lunate} fε{lunate} (0, x, v), x, v ∈ R3, our main purpose is to justify the global-in-time uniform energy estimates of fε{lunate} (t, x, v) in ε{lunate} and prove that fε{lunate} (t, x, v) converges strongly to f (t, x, v) whose dynamic is governed by the acoustic system. © 2009 Elsevier Inc. All rights reserved.

Research Area(s)

  • Acoustic limit, Boltzmann equation, Cauchy problem, Landau equation

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