Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T15:37:24.698Z Has data issue: false hasContentIssue false
  • English
  • Français

On blow-up of solution for Euler equations

Published online by Cambridge University Press:  15 April 2002

Eric Behr ,
Jindřich Nečas  and
Hongyou Wu
Eric Behr
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA.
Jindřich Nečas
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA.
Hongyou Wu
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA.
Get access

Abstract

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

Keywords

Euler equationsblow-up of solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 2 , March 2001 , pp. 229 - 238
Copyright
© EDP Sciences, SMAI, 2001

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bellout, H., Necas, J. and Rajagopal, K.R., On the existence and uniqueness of flows of multipolar fluids of grade 3 and their stability. Internat. J. Engrg. Sci. 37 (1999) 75-96. CrossRef
Delort, J.-M., Estimations fines pour des opérateurs pseudo-différentiels analytiques sur un ouvert à bord de $\xR^n$ application aux equations d'Euler. Comm. Partial Differential Equations 10 (1985) 1465-1525. CrossRef
Grauer, R. and Sideris, T., Numerical computation of three dimensional incompressible ideal fluids with swirl. Phys. Rev. Lett. 67 (1991) 3511. CrossRef
Grauer, R. and Sideris, T., Finite time singularities in ideal fluids with swirl. Phys. D 88 (1995) 116-132. CrossRef
E. Hille and R.S. Phillips, Functional analysis and semi-Groups. Amer. Math. Soc., Providence, R.I. (1957).
Kerr, R., Evidence for a singularity of the three-dimensional incompressible Euler equations. Phys. Fluids A5 (1993) 1725-1746. CrossRef
Leray, J., Sur le mouvement d'un liquide visqueux remplissant l'espace. Acta Math. 63 (1934) 193-248. CrossRef
P.-L. Lions, Mathematical topics in fluid mechanics, Vol. 1. Incompressible models. Oxford University Press, New York (1996).
Málek, J., Necas, J., Pokorný, M. and Schonbek, M., On possible singular solutions to the Navier-Stokes equations. Math. Nachr. 199 (1999) 97-114. CrossRef
J. Necas, Theory of multipolar fluids. Problems and methods in mathematical physics (Chemnitz, 1993) 111-119. Teubner, Stuttgart, Teubner-Texte Math. 134 (1994).
Necas, J., M. Růzicka and V. Sverák, 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.
Necas, J., M. Růzicka and V. Sverák, On Leray's self-similar solutions of the Navier-Stokes equations. Acta Math. 176 (1996) 283-294. CrossRef
Pumir, A. and Siggia, E., Collapsing solutions to the 3-D Euler equations. Phys. Fluids A2 (1990) 220-241. CrossRef
Pumir, A. and Siggia, E., Development of singular solutions to the axisymmetric Euler equations. Phys. Fluids A4 (1992) 1472-1491. CrossRef