On the Global Existence of Mild Solutions to the Boltzmann Equation for Small Data in LD

Research output: Contribution to journalArticlepeer-review

Abstract

We develop a new theory of existence of global solutions to the Boltzmann equation for small initial data. These new mild solutions are analogous to the mild solutions for the Navier-Stokes equations. The existence comes as a result of the study of the competing phenomena of dispersion, due to the transport operator, and of singularity formation, due to the nonlinear Boltzmann collision operator. It is the joint use of the so-called dispersive estimates with new convolution inequalities on the gain term of the collision operator that allows to obtain uniform bounds on the solutions and thus demonstrate the existence of solutions.

Original languageEnglish (US)
Pages (from-to)453-476
Number of pages24
JournalCommunications in Mathematical Physics
Volume302
Issue number2
DOIs
StatePublished - Mar 1 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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