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

Yoshinori Morimoto; Shota Sakamoto

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arXiv · 1512.00585

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

Yoshinori Morimoto·Shota Sakamoto

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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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Yoshinori Morimoto, Shota Sakamoto. 2015-12-02. Global solutions in the critical Besov space for the non cutoff Boltzmann equation. https://arxiv.org/abs/1512.00585

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