C Smoothing for Weak Solutions of the Inhomogeneous Landau Equation

Christopher Henderson, Stanley Snelson

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We consider the spatially inhomogeneous Landau equation with initial data that is bounded by a Gaussian in the velocity variable. In the case of moderately soft potentials, we show that weak solutions immediately become smooth, and remain smooth as long as the mass, energy, and entropy densities remain under control. For very soft potentials, we obtain the same conclusion with the additional assumption that a sufficiently high moment of the solution in the velocity variable remains bounded. Our proof relies on the iteration of local Schauder-type estimates.

Original languageEnglish (US)
Pages (from-to)113-143
Number of pages31
JournalArchive for Rational Mechanics and Analysis
Volume236
Issue number1
DOIs
StatePublished - Apr 1 2020
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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