Global solutions in the critical Besov space for the non cutoff Boltzmann equation

2015/12/02 by Yoshinori Morimoto, Morimoto, Yoshinori, Shota Sakamoto +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1512.00585

openalex publication_date 2015/12/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The Boltzmann equation is studied without the cutoff assumption. Under a perturbative setting, a unique global solution of the Cauchy problem of the equation is established in a critical Chemin-Lerner space. In order to analyse the collisional term of the equation, a Chemin-Lerner norm is combined with a non-isotropic norm with respect to a velocity variable, which yields an apriori estimate for an energy estimate. Together with local existence following from commutator estimates and the Hahn-Banach extension theorem, the desired solution is obtained. Also, the non-negativity of the solution is rigorously shown.

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