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.


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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