Global solutions for the critical Burgers equation in the Besov spaces and the large time behavior

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12 Citations (Scopus)

Abstract

Abstract We consider the Cauchy problem for the critical Burgers equation. The existence and the uniqueness of global solutions for small initial data are studied in the Besov space B0∞,1(ℝn) and it is shown that the global solutions are bounded in time. We also study the large time behavior of the solutions with the initial data u0∈L1(ℝn)∩B0∞,1(ℝn) to show that the solution behaves like the Poisson kernel.

Original languageEnglish
Pages (from-to)687-713
Number of pages27
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume32
Issue number3
DOIs
Publication statusPublished - 2015 May 1
Externally publishedYes

Keywords

  • Besov spaces
  • Burgers equation
  • Large time behavior
  • Poisson kernel

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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