An alternative energy bound derivation for a generalized Hasegawa-Mima equation

Jared C. Bronski, Razvan C. Fetecau

Research output: Contribution to journalArticlepeer-review


We present an alternative derivation of the H1-boundedness of solutions to a generalized Hasegawa-Mima equation, first investigated by Grauer (1998) [2]. We apply a Lyapunov function technique similar to the one used for constructing energy bounds for the KuramotoSivashinsky equation. Different from Grauer (1998) [2], who uses this technique in a Fourier space approach, we employ the physical space construction of the Lyapunov function, as developed in Bronski and Gambill (2006) [11]. Our approach has the advantage that it is more transparent in what concerns the estimates and the dominant terms that are being retained. A key tool of the present work, which replaces the algebraic manipulations on the Fourier coefficients from the other approach, is a HardyRellich type inequality.

Original languageEnglish (US)
Pages (from-to)1362-1368
Number of pages7
JournalNonlinear Analysis: Real World Applications
Issue number3
StatePublished - Jun 2012


  • Dissipative dynamics
  • Global attractors
  • KuramotoSivashinsky equation

ASJC Scopus subject areas

  • Analysis
  • Engineering(all)
  • Economics, Econometrics and Finance(all)
  • Computational Mathematics
  • Applied Mathematics


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