Global Well-Posedness of the Boltzmann Equation with Large Amplitude Initial Data

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journal

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Original languageEnglish
Pages (from-to)375-424
Journal / PublicationArchive for Rational Mechanics and Analysis
Issue number1
Publication statusPublished - 1 Jul 2017


The global well-posedness of the Boltzmann equation with initial data of large amplitude has remained a long-standing open problem. In this paper, by developing a new Lx∞Lv1∩Lx,v∞ approach, we prove the global existence and uniqueness of mild solutions to the Boltzmann equation in the whole space or torus for a class of initial data with bounded velocity-weighted L norm under some smallness condition on the Lx1Lv∞ norm as well as defect mass, energy and entropy so that the initial data allow large amplitude oscillations. Both the hard and soft potentials with angular cut-off are considered, and the large time behavior of solutions in the Lx,v∞ norm with explicit rates of convergence are also studied.