## 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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