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Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials. (English) Zbl 1113.82062
Summary: For the spatially homogeneous Boltzmann equation with hard potentials and Grad’s cutoff (e.g. hard spheres), we give quantitative estimates of exponential convergence to equilibrium, and we show that the rate of exponential decay is governed by the spectral gap for the linearized equation, on which we provide a lower bound. Our approach is based on establishing spectral gap-like estimates valid near the equilibrium, and then connecting the latter to the quantitative nonlinear theory. This leads us to an explicit study of the linearized Boltzmann collision operator in functional spaces larger than the usual linearization setting.

82C40 Kinetic theory of gases in time-dependent statistical mechanics
47N55 Applications of operator theory in statistical physics (MSC2000)
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