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math.APFeb 2, 2001
51
citations (OpenAlex)
authors
  • Diego Cordoba
  • Charles Fefferman
institutions
  • Princeton University
  • University of Chicago
arXiv abstractPDF
paper

On the Collapse of Tubes Carried by 3D Incompressible Flows

arXiv:math/0101253 · doi:10.1007/s002200100502

Abstract

We povide a test for numerical simulations for the collapse of regular tubes carried by a 3D incompressible flow. In particular, we obtain necessary conditions for 3D Euler to have a vortex tube collapse in finite time.

10 pages; the only change in this replacement is correction of " From" typos due to corruption in e-mail

References in corpus (1)

  • Scalars convected by a 2D incompressible flow

Cited by in corpus (9)

  • Quaternions and particle dynamics in the Euler fluid equations
  • Nonexistence of self-similar singularities for the 3D incompressible Euler equations
  • On the spectral dynamics of the deformation tensor and new a priori estimates for the 3D Euler equations
  • Incompressible Euler Equations: the blow-up problem and related results
  • Ortho-normal quaternion frames, Lagrangian evolution equations and the three-dimensional Euler equations
  • 3D Euler equations and ideal MHD mapped to regular systems: probing the finite-time blowup hypothesis
  • On the blow-up problem and new a priori estimates for the 3D Euler and the Navier-Stokes equations
  • Finite Time Blow-up of a 3D Model for Incompressible Euler Equations
  • On the apparition of singularities of vector fields transported by volume preserving diffeomorphisms
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