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Acoustic and Stokes limits for the Boltzmann equation. (English. Abridged French version) Zbl 0918.35109

Summary: The Boltzmann equation is considered over a periodic spatial domain for bounded collision kernels. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that converge entropically (and hence strongly in \(L^1\)) to a unique limit governed by a solution of the acoustic or Stokes equations, provided that its initial fluctuations converge entropically to an appropriate limit associated to any given \(L^2\) initial data of the acoustic or Stokes equations. The associated conservation laws are recovered in the limit.

MSC:

35Q35 PDEs in connection with fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C70 Transport processes in time-dependent statistical mechanics
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