Mathematics > Analysis of PDEs
[Submitted on 8 Dec 2009 (v1), last revised 27 Oct 2010 (this version, v3)]
Title:Global existence and full regularity of the Boltzmann equation without angular cutoff
View PDFAbstract:We prove the global existence and uniqueness of classical solutions around an equilibrium to the Boltzmann equation without angular cutoff in some Sobolev spaces. In addition, the solutions thus obtained are shown to be non-negative and $C^\infty$ in all variables for any positive time. In this paper, we study the Maxwellian molecule type collision operator with mild singularity. One of the key observations is the introduction of a new important norm related to the singular behavior of the cross section in the collision operator. This norm captures the essential properties of the singularity and yields precisely the dissipation of the linearized collision operator through the celebrated H-theorem.
Submission history
From: Radjesvarane Alexandre [view email] [via CCSD proxy][v1] Tue, 8 Dec 2009 07:37:00 UTC (44 KB)
[v2] Sun, 27 Dec 2009 18:11:44 UTC (46 KB)
[v3] Wed, 27 Oct 2010 07:38:33 UTC (48 KB)
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