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On the Lagrangian Dynamics for the 3D Incompressible Euler Equations

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Abstract

In this paper we study the dynamical behaviors along the particle trajectories for some quantities of the 3D inviscid incompressible fluids. We construct evolution equations satisfied by scalar quantities composed of spectrum of the deformation tensor, the hessian of the pressure and the direction field of the vorticity, and study the dichotomy between the finite time singularity and the long time behaviors of the various scalar quantities.

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea

    Dongho Chae

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  1. Dongho Chae
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Correspondence to Dongho Chae.

Additional information

Communicated by P. Constantin

The work was supported partially by the KOSEF Grant no. R01-2005-000-10077-0.

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Chae, D. On the Lagrangian Dynamics for the 3D Incompressible Euler Equations. Commun. Math. Phys. 269, 557–569 (2007). https://doi.org/10.1007/s00220-006-0129-7

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  • DOI: https://doi.org/10.1007/s00220-006-0129-7

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