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arXiv · 2212.04315

Non-cutoff Boltzmann equation with soft potentials in the whole space

Kleber Carrapatoso·Pierre Gervais
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Abstract

We prove the existence and uniqueness of global solutions to the Boltzmann equation with non-cutoff 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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Kleber Carrapatoso, Pierre Gervais. 2022-12-08. Non-cutoff Boltzmann equation with soft potentials in the whole space. https://doi.org/10.2140/paa.2024.6.253

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