Abstract
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.
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Duan, R., Liu, S. & Xu, J. Global Well-Posedness in Spatially Critical Besov Space for the Boltzmann Equation. Arch Rational Mech Anal 220, 711–745 (2016). https://doi.org/10.1007/s00205-015-0940-4
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DOI: https://doi.org/10.1007/s00205-015-0940-4