On blow-up of solution for Euler equations
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 (2001) no. 2, pp. 229-238.

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.

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.

Classification: 35Q05
Keywords: Euler equations, blow-up of solution
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Behr, Eric; Nečas, Jindřich; Wu, Hongyou. On blow-up of solution for Euler equations. ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 (2001) no. 2, pp. 229-238. http://www.numdam.org/item/M2AN_2001__35_2_229_0/

[1] H. Bellout, J. Nečas and K.R. Rajagopal, On the existence and uniqueness of flows of multipolar fluids of grade 3 and their stability. Internat. J. Engrg. Sci. 37 (1999) 75-96.

[2] J.-M. Delort, Estimations fines pour des opérateurs pseudo-différentiels analytiques sur un ouvert à bord de n application aux equations d’Euler. Comm. Partial Differential Equations 10 (1985) 1465-1525. | Zbl

[3] R. Grauer and T. Sideris, Numerical computation of three dimensional incompressible ideal fluids with swirl. Phys. Rev. Lett. 67 (1991) 3511.

[4] R. Grauer and T. Sideris, Finite time singularities in ideal fluids with swirl. Phys. D 88 (1995) 116-132. | Zbl

[5] E. Hille and R.S. Phillips, Functional analysis and semi-Groups. Amer. Math. Soc., Providence, R.I. (1957). | MR | Zbl

[6] R. Kerr, Evidence for a singularity of the three-dimensional incompressible Euler equations. Phys. Fluids A5 (1993) 1725-1746. | Zbl

[7] J. Leray, Sur le mouvement d'un liquide visqueux remplissant l'espace. Acta Math. 63 (1934) 193-248. | JFM

[8] P.-L. Lions, Mathematical topics in fluid mechanics, Vol. 1. Incompressible models. Oxford University Press, New York (1996). | MR | Zbl

[9] J. Málek, J. Nečas, M. Pokorný and M. Schonbek, On possible singular solutions to the Navier-Stokes equations. Math. Nachr. 199 (1999) 97-114. | Zbl

[10] J. Nečas, Theory of multipolar fluids. Problems and methods in mathematical physics (Chemnitz, 1993) 111-119. Teubner, Stuttgart, Teubner-Texte Math. 134 (1994). | Zbl

[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. | Zbl

[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. | Zbl

[13] A. Pumir and E. Siggia, Collapsing solutions to the 3-D Euler equations. Phys. Fluids A2 (1990) 220-241. | Zbl

[14] A. Pumir and E. Siggia, Development of singular solutions to the axisymmetric Euler equations. Phys. Fluids A4 (1992) 1472-1491. | Zbl