Corpus ID: 237513385

On the role of continuous symmetries in the solution of the 3D Euler fluid equations and related models

  title={On the role of continuous symmetries in the solution of the 3D Euler fluid equations and related models},
  author={M. Bustamante},
We review the continuous symmetry approach and apply it to find the solution, via the construction of constants of motion and infinitesimal symmetries, of the 3D Euler fluid equations in several instances of interest, without recourse to Noether’s theorem. We show that the vorticity field is a symmetry of the flow and therefore one can construct a Lie algebra of symmetries if the flow admits another symmetry. For steady Euler flows this leads directly to the distinction of (non-)Beltrami flows… Expand


Symmetry-plane model of 3D Euler flows and mapping to regular systems to improve blowup assessment using numerical and analytical solutions
Motivated by the work on stagnation-point-type exact solutions (with infinite energy) of 3D Euler fluid equations by Gibbon et al. (Physica D, vol. 132 (4), 1999, pp. 497–510) and the subsequentExpand
Geometric formulation of the Cauchy invariants for incompressible Euler flow in flat and curved spaces
Cauchy invariants are now viewed as a powerful tool for investigating the Lagrangian structure of three-dimensional (3D) ideal flow (Frisch & Zheligovsky, Commun. Math. Phys., vol. 326, 2014, pp.Expand
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3D Euler in a 2D Symmetry Plane
Initial results from new calculations of interacting anti-parallel Euler vortices are presented. The objective is to understand the origins of singular scaling presented by Kerr (1993) with differentExpand
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Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
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Numerical study of singularity formation in a class of Euler and Navier–Stokes flows
We study numerically a class of stretched solutions of the three-dimensional Euler and Navier–Stokes equations identified by Gibbon, Fokas, and Doering (1999). Pseudo-spectral computations of a EulerExpand
Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem.
  • M. Bustamante, M. Brachet
  • Mathematics, Physics
  • Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2012
The main conclusion is that the numerical results are not inconsistent with a singularity but that higher-resolution studies are needed to extend the time interval on which a well-resolved power-law behavior of δ(t) takes place and check whether the new regime is genuine and not simply a crossover to a faster exponential decay. Expand