Acoustic limit of the Boltzmann equation: classical solutions

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dc.creatorJang, Juhi
dc.creatorJiang, Ning
dc.date2009-04-28
dc.date.accessioned2026-07-07T13:09:29Z
dc.date.available2026-07-07T13:09:29Z
dc.descriptionWe study the acoustic limit from the Boltzmann equation in the framework of classical solutions. For a solution $F_\varepsilon=μ+\varepsilon \sqrtμf_\varepsilon$ to the rescaled Boltzmann equation in the acoustic time scaling \partial_t F_\varepsilon +\vgrad F_\varepsilon =\frac{1}{\varepsilon} \Q(F_\varepsilon,F_\varepsilon), inside a periodic box $\mathbb{T}^3$, we establish the global-in-time uniform energy estimates of $f_\varepsilon$ in $\varepsilon$ and prove that $f_\varepsilon$ converges strongly to $f$ whose dynamics is governed by the acoustic system. The collision kernel $\Q$ includes hard-sphere interaction and inverse-power law with an angular cutoff.
dc.description14 pages, To appear on Discrete and Continuous Dynamical Systems - Series A
dc.identifierhttps://arxiv.org/abs/0904.4459
dc.identifierhttp://arxiv.org/abs/0904.4459
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/228749
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.titleAcoustic limit of the Boltzmann equation: classical solutions
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