On Measure Solutions of the Boltzmann Equation, part I: Moment Production and Stability Estimates
نویسنده
چکیده
The spatially homogeneous Boltzmann equation with hard potentials is considered for measure valued initial data having finite mass and energy. We prove the existence of weak measure solutions, with and without angular cutoff on the collision kernel; the proof in particular makes use of an approximation argument based on the Mehler transform. Moment production estimates in the usual form and in the exponential form are obtained for these solutions. Finally for the Grad angular cutoff, we also establish uniqueness and strong stability estimate on these solutions. Mathematics Subject Classification (2000): 35Q Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05], 76P05 Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05].
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