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Gevrey Regularity for a Class of Solutions of the Linearized Spatially Homogeneous Boltzmann Equation Without Angular Cutoff

Volume 12, Number 1 (2011), 100 - 112

Gevrey Regularity for a Class of Solutions of the Linearized Spatially Homogeneous Boltzmann Equation Without Angular Cutoff

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Abstract

In this paper, we study the Gevrey smoothing property for the non-negative solution of the linearized spatially homogeneous Boltzmann equation. Using pseudo-differential calculus and some techniques of mathematical analysis, we show that in the non-cutoff and non-Maxwellian case with the inverse power law potential, if the solution is Lipschitz continuous on the velocity variable, then it has the local Gevrey regularity.