On blow-up of solution for Euler equations

Eric Behr; Jindřich Nečas; Hongyou Wu

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2001)

  • Volume: 35, Issue: 2, page 229-238
  • ISSN: 0764-583X

Abstract

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We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.

How to cite

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Behr, Eric, Nečas, Jindřich, and Wu, Hongyou. "On blow-up of solution for Euler equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 35.2 (2001): 229-238. <http://eudml.org/doc/194048>.

@article{Behr2001,
abstract = {We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.},
author = {Behr, Eric, Nečas, Jindřich, Wu, Hongyou},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Euler equations; blow-up of solution; approximate solutions; Taylor polynomials},
language = {eng},
number = {2},
pages = {229-238},
publisher = {EDP-Sciences},
title = {On blow-up of solution for Euler equations},
url = {http://eudml.org/doc/194048},
volume = {35},
year = {2001},
}

TY - JOUR
AU - Behr, Eric
AU - Nečas, Jindřich
AU - Wu, Hongyou
TI - On blow-up of solution for Euler equations
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2001
PB - EDP-Sciences
VL - 35
IS - 2
SP - 229
EP - 238
AB - We present numerical evidence for the blow-up of solution for the Euler equations. Our approximate solutions are Taylor polynomials in the time variable of an exact solution, and we believe that in terms of the exact solution, the blow-up will be rigorously proved.
LA - eng
KW - Euler equations; blow-up of solution; approximate solutions; Taylor polynomials
UR - http://eudml.org/doc/194048
ER -

References

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  11. [11] J. Nečas, M. Růžička and V. Šverák, Sur une remarque de J. Leray concernant la construction de solutions singulières des équations de Navier-Stokes. C. R. Acad. Sci. Paris Sér. I Math. 323 (1996) 245–249. Zbl0859.35091
  12. [12] J. Nečas, M. Růžička and V. Šverák, On Leray’s self-similar solutions of the Navier-Stokes equations. Acta Math. 176 (1996) 283–294. Zbl0884.35115
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  14. [14] A. Pumir and E. Siggia, Development of singular solutions to the axisymmetric Euler equations. Phys. Fluids A4 (1992) 1472–1491. Zbl0825.76121

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