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Global well-posedness in spatially critical Besov space for the Boltzmann equation. (English) Zbl 1334.35199

Summary: The unique global strong solution in the Chemin-Lerner type space to the Cauchy problem on the Boltzmann equation for hard potentials is constructed in a perturbation framework. Such a solution space is of critical regularity with respect to the spatial variable, and it can capture the intrinsic properties of the Boltzmann equation. For the proof of global well-posedness, we develop some new estimates on the nonlinear collision term through the Littlewood-Paley theory.

MSC:

35Q20 Boltzmann equations
42B25 Maximal functions, Littlewood-Paley theory
35B65 Smoothness and regularity of solutions to PDEs
35D35 Strong solutions to PDEs
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