New numerical results for the surface quasi-geostrophic equation

Peter Constantin, Ming Chih Lai, Ramjee Sharma, Yu Hou Tseng, Jiahong Wu

Research output: Contribution to journalArticle

28 Scopus citations

Abstract

The question whether classical solutions of the surface quasi-geostrophic (SQG) equation can develop finite-time singularities remains open. This paper presents new numerical computations of the solutions to the SQG equation corresponding to several classes of initial data previously proposed by Constantin et al. (Nonlinearity 7:1495-1533, 1994). By parallelizing the serial pseudo-spectral codes through slab decompositions and applying suitable filters, we are able to simulate these solutions with great precision and on large time intervals. These computations reveal detailed finite-time behavior, large-time asymptotics and key parameter dependence of the solutions and provide information for further investigations on the global regularity issue concerning the SQG equation.

Original languageEnglish (US)
Pages (from-to)1-28
Number of pages28
JournalJournal of Scientific Computing
Volume50
Issue number1
DOIs
StatePublished - Jan 1 2012

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Engineering(all)
  • Computational Theory and Mathematics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Global regularity
  • Parallel computation
  • Surface quasi-geostrophic equation

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