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Noncutoff Boltzmann
equation with soft potentials in the whole space
Kleber Carrapatoso and Pierre Gervais |
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Vol. 6 (2024), No. 1, 253–303
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DOI: 10.2140/paa.2024.6.253
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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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Authors |
| Kleber Carrapatoso | |
| Centre de Mathématiques Laurent
Schwartz École Polytechnique, Institut Polytechnique de Paris Palaiseau France |
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| Pierre Gervais | |
| Department of Economics, Social
Sciences, Applied Mathematics and Statistics Università degli Studi di Torino Torino Italy |
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| © 2024 MSP (Mathematical Sciences Publishers). |
