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Zbl 1170.35500
Saint-Raymond, Laure
Hydrodynamic limits: Some improvements of the relative entropy method. (English)
[J] Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 3, 705-744 (2009). ISSN 0294-1449

Summary: The present paper is devoted to the study of the incompressible Euler limit of the Boltzmann equation via the relative entropy method. It extends the convergence result for well-prepared initial data obtained by the author in [Arch. Ration. Mech. Anal. 166, No.~1, 47--80 (2003; Zbl 1016.76071)]. It explains especially how to take into account the acoustic waves and relaxation layer, and thus to obtain convergence results under weak assumptions on the initial data.\par The study presented here requires in return some nonuniform control on the large tails of the distribution, which is satisfied for instance by the classical solutions close to a Maxwellian built by {\it Y. Guo} [Commun. Pure Appl. Math. 55, No.~9, 1104--1135 (2002; Zbl 1027.82035)].

MSC 2000:: *35Q35 Other equations arising in fluid mechanics
76P05 Molecular or atomic structure
76Q05 Density waves (fluid mechanics)

Keywords: incompressible Euler equations; Boltzmann equation; hydrodynamic limits; relaxation layer; acoustic waves; relative entropy method

Citations: Zbl 1016.76071; Zbl 1027.82035

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