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

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.

preprint2015arXivOpen access
Yoshinori MorimotoShota Sakamoto
math.AP
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Open access2 authors1 topic
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Yoshinori MorimotoShota Sakamoto

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