Abstract

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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