Nous présentons une solution numérique des équations d'Euler montrant la solution non-bornée : l'approximation de la solution est donnée par une série de Taylor dans la variable de temps de la solution exacte, et il est probable que cet exemple fournira le résultat.
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.
@article{M2AN_2001__35_2_229_0, author = {Behr, Eric and Ne\v cas, Jind\v rich and Wu, Hongyou}, title = {On blow-up of solution for Euler equations}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique}, volume = {35}, year = {2001}, pages = {229-238}, mrnumber = {1825697}, zbl = {0985.35057}, language = {en}, url = {http://dml.mathdoc.fr/item/M2AN_2001__35_2_229_0} }
Behr, Eric; Nečas, Jindřich; Wu, Hongyou. On blow-up of solution for Euler equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 229-238. http://gdmltest.u-ga.fr/item/M2AN_2001__35_2_229_0/
[1] On the existence and uniqueness of flows of multipolar fluids of grade and their stability. Internat. J. Engrg. Sci. 37 (1999) 75-96.
, and ,[2] Estimations fines pour des opérateurs pseudo-différentiels analytiques sur un ouvert à bord de application aux equations d’Euler. Comm. Partial Differential Equations 10 (1985) 1465-1525. | Zbl 0594.35118
,[3] Numerical computation of three dimensional incompressible ideal fluids with swirl. Phys. Rev. Lett. 67 (1991) 3511.
and ,[4] Finite time singularities in ideal fluids with swirl. Phys. D 88 (1995) 116-132. | Zbl 0899.76286
and ,[5] Functional analysis and semi-Groups. Amer. Math. Soc., Providence, R.I. (1957). | MR 89373 | Zbl 0078.10004
and ,[6] Evidence for a singularity of the three-dimensional incompressible Euler equations. Phys. Fluids A5 (1993) 1725-1746. | Zbl 0800.76083
,[7] Sur le mouvement d'un liquide visqueux remplissant l'espace. Acta Math. 63 (1934) 193-248. | JFM 60.0726.05
,[8] Mathematical topics in fluid mechanics, Vol. 1. Incompressible models. Oxford University Press, New York (1996). | MR 1422251 | Zbl 0866.76002
,[9] On possible singular solutions to the Navier-Stokes equations. Math. Nachr. 199 (1999) 97-114. | Zbl 0922.35126
, , and ,[10] Theory of multipolar fluids. Problems and methods in mathematical physics (Chemnitz, 1993) 111-119. Teubner, Stuttgart, Teubner-Texte Math. 134 (1994). | Zbl 0815.76009
,[11] 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. | Zbl 0859.35091
, and ,[12] On Leray's self-similar solutions of the Navier-Stokes equations. Acta Math. 176 (1996) 283-294. | Zbl 0884.35115
, and ,[13] Collapsing solutions to the 3-D Euler equations. Phys. Fluids A2 (1990) 220-241. | Zbl 0696.76070
and ,[14] Development of singular solutions to the axisymmetric Euler equations. Phys. Fluids A4 (1992) 1472-1491. | Zbl 0825.76121
and ,