Local solutions of the Landau equation with rough, slowly decaying initial data

Christopher Henderson, Stanley Snelson, Andrei Tarfulea

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform polynomial decay in the velocity variable, and that satisfies a technical lower bound assumption (but can have vacuum regions). For uniqueness in this weak class, we have to make the additional assumption that the initial data is Hölder continuous. Our hypotheses are much weaker, in terms of regularity and decay, than previous large-data well-posedness results in the literature. We also derive a continuation criterion for our solutions that is, for the case of very soft potentials, an improvement over the previous state of the art.

Original languageEnglish (US)
Pages (from-to)1345-1377
Number of pages33
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number6
DOIs
StatePublished - Nov 1 2020

Keywords

  • Classical solutions
  • Kinetic equations
  • Landau equation
  • Large data well-posedness
  • Vacuum regions

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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