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From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system. (English) Zbl 1304.35476

Summary: We establish a Navier-Stokes-Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak solution of a Navier-Stokes-Fourier system for all time.

MSC:

35Q20 Boltzmann equations
35Q35 PDEs in connection with fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
82C40 Kinetic theory of gases in time-dependent statistical mechanics
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