Remarks on Type I Blow-Up for the 3D Euler Equations and the 2D Boussinesq Equations

Dongho Chae, Peter Constantin

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2 Scopus citations

Abstract

In this paper, we derive kinematic relations for quantities involving the rate of strain tensor and the Hessian of the pressure for solutions of the 3D Euler equations and the 2D Boussinesq equations. Using these kinematic relations, we prove new blow-up criteria and obtain conditions for the absence of type I singularity for these equations. We obtain both global and localized versions of the results. Some of the new blow-up criteria and type I conditions improve previous results of Chae and Constantin (Int Math Res Notices rnab014, 2021).

Original languageEnglish (US)
Article number77
JournalJournal of Nonlinear Science
Volume31
Issue number5
DOIs
StatePublished - Oct 2021

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • General Engineering
  • Applied Mathematics

Keywords

  • Blow-up criterion
  • Boussinesq equations
  • Euler equations
  • Kinematic relations
  • Type I singularity

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