English

Remarks on type I blow up for the 3D Euler equations and the 2D Boussinesq equations

Analysis of PDEs 2021-08-04 v1

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 [3].

Keywords

Cite

@article{arxiv.2103.10672,
  title  = {Remarks on type I blow up for the 3D Euler equations and the 2D Boussinesq equations},
  author = {Dongho Chae and Peter Constantin},
  journal= {arXiv preprint arXiv:2103.10672},
  year   = {2021}
}

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14 pages