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Noncutoff Boltzmann equation with soft potentials in the whole space

Kleber Carrapatoso and Pierre Gervais

Vol. 6 (2024), No. 1, 253–303
DOI: 10.2140/paa.2024.6.253

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.

Boltzmann equation, noncutoff kernels, soft-potentials, large-time behavior
Mathematical Subject Classification
Primary: 35Q20
Secondary: 82C40, 76P05
Received: 17 March 2023
Revised: 23 June 2023
Accepted: 18 October 2023
Published: 22 February 2024
Kleber Carrapatoso
Centre de Mathématiques Laurent Schwartz
École Polytechnique, Institut Polytechnique de Paris
Pierre Gervais
Department of Economics, Social Sciences, Applied Mathematics and Statistics
Università degli Studi di Torino