On the regularity of the De Gregorio model for the 3D Euler equations

  • Jiajie Chen

    California Institute of Technology, Pasadena, USA; New York University, USA
On the regularity of the De Gregorio model for the 3D Euler equations cover

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Abstract

We study the regularity of the De Gregorio (DG) model on for initial data with period and in class : is odd and (or ) on . These sign and symmetry properties are the same as those of the smooth initial data that lead to singularity formation of the De Gregorio model on or the generalized Constantin–Lax–Majda (gCLM) model on or with a positive parameter. Thus, to establish global regularity of the DG model for general smooth initial data, which is a conjecture on the DG model, an important step is to rule out potential finite time blowup from smooth initial data in . We accomplish this by establishing a one-point blowup criterion and proving global well-posedness for initial data with . On the other hand, for any , we construct a finite time blowup solution from a class of initial data with . Our results imply that singularities developed in the DG model and the gCLM model on can be prevented by stronger advection.

Cite this article

Jiajie Chen, On the regularity of the De Gregorio model for the 3D Euler equations. J. Eur. Math. Soc. (2023), published online first

DOI 10.4171/JEMS/1399