Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation

José A. Carrillo, Lucas C.F. Ferreira

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions. While the only small self-similar solution in the strong ℒp space is the null solution, infinitely many self-similar solutions do exist in weak- ℒp spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. © Springer-Verlag 2007.
Original languageEnglish
Pages (from-to)111-142
JournalMonatshefte fur Mathematik
Volume151
DOIs
Publication statusPublished - 1 Jun 2007

Keywords

  • Long time asymptotics
  • Quasi-geostrophic equation
  • Self-similar solutions

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