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From the Boltzmann equation to the Stokes-Fourier system in a bounded domain. (English) Zbl 1024.35031

Summary: We prove that the renormalized solutions of the Boltzmann equation considered in a bounded domain with different types of (kinetic) boundary conditions converge to the Stokes-Fourier system with different types of (fluid) boundary conditions when the main free path goes to zero. This extends the work of F. Golse and C. D. Levermore [ibid. 55, 336-393 (2002; Zbl 1044.76055)] to the case of a bounded domain.

MSC:

35F25 Initial value problems for nonlinear first-order PDEs
35Q35 PDEs in connection with fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics

Citations:

Zbl 1044.76055
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