The Boltzmann equation with a soft potential - I. Linear, spatially-homogeneous

Russel Caflisch

Research output: Contribution to journalArticle

Abstract

The initial value problem for the linearized spatially-homogeneous Boltzmann equation has the form ∂f/∂t+Lf=0 with f(ξ, t=0) given. The linear operator L operates only on the ξ variable and is non-negative, but, for the soft potentials considered here, its continuous spectrum extends to the origin. Thus one cannot expect exponential decay for f, but in this paper it is shown that f decays like etβ with β<1. This result will be used in Part II to show existence of solutions of the initial value problem for the full nonlinear, spatially dependent problem for initial data that is close to equilibrium.

Original languageEnglish (US)
Pages (from-to)71-95
Number of pages25
JournalCommunications in Mathematical Physics
Volume74
Issue number1
DOIs
StatePublished - Feb 1980

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Boltzmann Equation
boundary value problems
Initial Value Problem
linear operators
Continuous Spectrum
continuous spectra
decay
Exponential Decay
Linear Operator
Existence of Solutions
Non-negative
Decay
Dependent
Form

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

The Boltzmann equation with a soft potential - I. Linear, spatially-homogeneous. / Caflisch, Russel.

In: Communications in Mathematical Physics, Vol. 74, No. 1, 02.1980, p. 71-95.

Research output: Contribution to journalArticle

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