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

Kleber Carrapatoso (1) , Pierre Gervais (2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Analyse (DMA)

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.

Domaines: Equations aux dérivées partielles [math.AP]

Kleber Carrapatoso, Pierre Gervais. Non-cutoff Boltzmann equation with soft potentials in the whole space. 2023. ⟨hal-03920195⟩