Analyticity and large time behavior for the Burgers equation and the quasi-geostrophic equation, the both with the critical dissipation

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Abstract

This paper is concerned with the Cauchy problem of the Burgers equation with the critical dissipation. The well-posedness and analyticity in both of the space and the time variables are studied based on the frequency decomposition method. The large time behavior is revealed for any large initial data. As a result, it is shown that any smooth and integrable solution is analytic in space and time as long as time is positive and behaves like the Poisson kernel as time tends to infinity. The corresponding results are also obtained for the quasi-geostrophic equation.

Original languageEnglish
Pages (from-to)855-876
Number of pages22
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume37
Issue number4
DOIs
Publication statusPublished - 2020 Jul 1

Keywords

  • Analyticity in space and time
  • Burgers equation
  • Critical dissipation
  • Large data
  • Large time behavior
  • Quasi-geostrophic equation

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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