The acoustic limit for the Boltzmann equation. (English) Zbl 0973.76075

First, the authors derive acoustic equations directly from the Boltzmann equation as a formal limit of moment equations for an appropriately scaled family of Boltzmann solutions. Then this limit is investigated for the Boltzmann equation considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of Di Perma-Lions renormalized solutions are shown to have fluctuations that converge entropically to a unique limit described by a solution of acoustic equations for all time, provided that its initial fluctuations converge entropically to an limit associated to any given \(L^2\) initial data of acoustic equations. The associated local conservation laws are recovered in this limit.


76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76A02 Foundations of fluid mechanics
45K05 Integro-partial differential equations
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