Skip to main content
Article thumbnail
Location of Repository

A sufficient condition for a finite-time $L_2 $ singularity of the 3d Euler Equations

By Xinyu He

Abstract

A sufficient condition is derived for a finite-time $L_2 $ singularity of the 3d incompressible Euler equations, making appropriate assumptions on eigenvalues of the Hessian of pressure. Under this condition $ \ \lim_{ t \uparrow T_*} \sup \|\frac{ D \omega} { Dt}\|_{L_2(\Omega)} = \infty $, where $\Omega \subset \mathbb{R}$ moves with the fluid. In particular, $| \omega | $, $| \S_{ij} | $, and $| \P_{ij} | $ all become unbounded at one point $(x_1, T_1) $, $T_1 $ being the first blow-up time in $L_2 $

Topics: QA
Publisher: Cambridge University Press
Year: 2005
OAI identifier: oai:wrap.warwick.ac.uk:737

Suggested articles

Citations

  1. (2002). A quaternionic structure in the 3d Euler and ideal MHD equations. doi
  2. (1999). An invariant for the 3d Euler equations. doi
  3. (1993). Eigenvalue problems in 3d Euler flows. doi
  4. (1993). Evidence for a singularity of the 3d, incompressible Euler equations. doi
  5. (1994). Geometric and analytical studies in turbulence. doi
  6. (1996). Geometric constraints on potentially singular solutions for the 3d Euler equations. doi
  7. (1985). Remarks on a paper by doi
  8. (1984). Remarks on the breakdown of smooth solutions for the 3d Euler equations. doi
  9. (2000). Stretching and compression of vorticity in the 3d Euler equations.
  10. (2001). Symmetry and the hydrodynamic blow-up problem. doi
  11. (2000). The interaction of skewed vortex pairs: a model for blow-up of the Navier– Stokes equations. doi
  12. (1986). Vorticity and the mathematical theory of incompressible fluid flow. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.