Acoustic limit for the Boltzmann equation in the whole space
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Detail(s)
Original language | English |
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Pages (from-to) | 7-19 |
Journal / Publication | Journal of Mathematical Analysis and Applications |
Volume | 367 |
Issue number | 1 |
Publication status | Published - 1 Jul 2010 |
Externally published | Yes |
Link(s)
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
Bibliographic Note
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Citation Format(s)
Acoustic limit for the Boltzmann equation in the whole space. / Liu, Shuangqian.
In: Journal of Mathematical Analysis and Applications, Vol. 367, No. 1, 01.07.2010, p. 7-19.
In: Journal of Mathematical Analysis and Applications, Vol. 367, No. 1, 01.07.2010, p. 7-19.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review