Global classical solutions of the Boltzmann equation without angular cut-off
نویسندگان
چکیده
منابع مشابه
Global Classical Solutions of the Boltzmann Equation without Angular Cut-off
This work proves the global stability of the Boltzmann equation (1872) with the physical collision kernels derived by Maxwell in 1866 for the full range of inverse-power intermolecular potentials, r−(p−1) with p > 2, for initial perturbations of the Maxwellian equilibrium states, as announced in [48]. We more generally cover collision kernels with parameters s ∈ (0, 1) and γ satisfying γ > −n i...
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This is a brief announcement of our recent proof of global existence and rapid decay to equilibrium of classical solutions to the Boltzmann equation without any angular cutoff, that is, for long-range interactions. We consider perturbations of the Maxwellian equilibrium states and include the physical cross-sections arising from an inverse-power intermolecular potential r(-(p-1)) with p > 2, an...
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A model Boltzmann equation (see formulas (1.1.6) { (1.1.9) below) without Grad's angular cutoo assumption is considered. One proves 1. the instantaneous smoothing in both position and velocity variables by the evolution semigroup associated to the Cauchy problem for this model; 2. the derivation of the analogue of the Landau-Fokker-Planck equation in the limit when grazing collisions prevail.
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In this paper we study the large-time behavior of perturbative classical solutions to the hard and soft potential Boltzmann equation without the angular cut-off assumption in the whole space Rx with n ≥ 3. We use the existence theory of global in time nearby Maxwellian solutions from [13,14]. It has been a longstanding open problem to determine the large time decay rates for the soft potential ...
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ژورنال
عنوان ژورنال: Journal of the American Mathematical Society
سال: 2011
ISSN: 0894-0347,1088-6834
DOI: 10.1090/s0894-0347-2011-00697-8