Energy method for Boltzmann equation

By Tai-Ping Liu, Tong Yang, Shih-Hsien Yu. 2004

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Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, methodology): “For completeness we also refer to a recent preprint dealing with the problem in whole space [22] and the article [25] for a related non-linear energy method.”
Global classical solutions of the Boltzmann equation without angular cut-off (2009, methodology): “We also mention recent methods introduced in the linearized regime by Guo [32] in 2003 and Liu-Yang-Yu [38] in 2004.”
Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “Comparing to the cutoff case, we aim to settle a mathematical framework similar to the studies first proved by Ukai, see [67,68], and fitted into an energy method by Liu and collaborators [52, 53 ] and Guo [46] which has led to a clean theory for the Cauchy problem in the cutoff case, for solutions ”
Decay of Dissipative Equations and Negative Sobolev Spaces (2011, background): “The existence of global solutions near Maxwellians has been established in various function spaces, see [31, 26, 28, 9, 20, 32, 10] for instance.”