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Abstract
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We prove the existence, uniqueness and convergence of global solutions to the
Boltzmann equation with noncutoff soft potentials in the whole space when the
initial data is a small perturbation of a Maxwellian with polynomial decay in
velocity. Our method is based in the decomposition of the desired solution into
two parts: one with polynomial decay in velocity satisfying the Boltzmann
equation with only a dissipative part of the linearized operator, the other with
Gaussian decay in velocity verifying the Boltzmann equation with a coupling
term.
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Keywords
Boltzmann equation, noncutoff kernels, soft-potentials,
large-time behavior
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Mathematical Subject Classification
Primary: 35Q20
Secondary: 82C40, 76P05
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Milestones
Received: 17 March 2023
Revised: 23 June 2023
Accepted: 18 October 2023
Published: 22 February 2024
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