An incompressible 2D didactic model with singularity and explicit solutions of the 2D Boussinesq equations

Dongho Chae, Peter Constantin, Jiahong Wu

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.

Original languageEnglish (US)
Pages (from-to)473-480
Number of pages8
JournalJournal of Mathematical Fluid Mechanics
Volume16
Issue number3
DOIs
StatePublished - Jan 1 2014

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • 2D Boussinesq equations
  • Explicit solutions
  • Inviscid model
  • Singularity

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