Exponential Decay for Soft Potentials near Maxwellian

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Global Existence and Full Regularity of the Boltzmann Equation Without Angular Cutoff (2009, methodology): “. We also note that his method has been generalized to various directions. Among them, a few are the external force case [35, 37], the Vlassov-Maxwell-Boltzmann equation [65], the soft potential case [66, 74] and the Landau equation [45, 74]. Independently of his method which is based on the macro-m”
Decay and Continuity of the Boltzmann Equation in Bounded Domains (2008, result): “Lemma 7 gives refined estimates for the operator Kw with w ∽ � −1/2 .Similar estimates were established in [ SG ].”
Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus (2006, background): “akened, which happens for interactions with “weak collision eﬀect” such as soft potentials (see for instance in [32]), one expects convergence rates of the form e−tτ with τ < 1 (see the results in [38]). The kernel of L in L2 v, which is composed of functions belonging to N(L) for any x, correspo”
Hypocoercive Diffusion Operators (2006, methodology): “Even in a close-to-equilibrium regime, decay estimates based on a linearization method are quite hard to obtain, and were not available at the time when [5] was published; since then this gap has been filled in a series of important works by Yan Guo and Robert Strain [13], [14].”