Chen, Zili Smooth solutions to the BGK equation and the ES-BGK equation with infinite energy. (English) Zbl 1394.35509 J. Differ. Equations 265, No. 1, 389-416 (2018). Summary: The BGK model and the ES-BGK model of the Boltzmann equation are of great importance in the kinetic theory of rarefied gases. For the Cauchy problems with general initial data, smooth solutions were obtained only in bounded domains for both models. In this paper, we establish the existence and uniqueness of smooth solutions in the whole space. More important, some smooth solutions can permit infiniteness of energy. Cited in 4 Documents MSC: 35Q83 Vlasov equations 35F25 Initial value problems for nonlinear first-order PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 82C40 Kinetic theory of gases in time-dependent statistical mechanics 35B65 Smoothness and regularity of solutions to PDEs 35Q20 Boltzmann equations Keywords:BGK model; ES-BGK model; smooth solution; infinite energy PDFBibTeX XMLCite \textit{Z. Chen}, J. Differ. Equations 265, No. 1, 389--416 (2018; Zbl 1394.35509) Full Text: DOI References: [1] Andries, P.; Bourgat, J.-F.; Le Tallec, P.; Perthame, B., Numerical comparison between the Boltzmann and ES-BGK models for rarefied gases, Comput. Methods Appl. Mech. Engrg., 191, 31, 3369-3390 (2002) · Zbl 1101.76377 [2] Andries, P.; Le Tallec, P.; Perlat, J.-P.; Perthame, B., The Gaussian-BGK model of Boltzmann equation with small Prandtl number, Eur. J. Mech. 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