Comptes Rendus
no. 5-6
Partial Differential Equations
Existence of topologically cylindrical shocks
[Existence des chocs topologiquement cylindrique]

Présenté par : Jean-Michel Bony

Nicola Costanzino1
1 Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA
Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 283-286.

Dans cette Note la stabilité multidimensionnelle des chocs cylindrique et de l'existence d'une structure perturbée voisine est présentée. Ceci fournit un exemple explicite d'une structure non planairepour laquelle la condition de stabilité uniforme de Kreiss–Lopatinsky–Majda est satisfaite.

In this Note the multidimensional stability of cylindrical shock profiles and the existence of a nearby perturbed structure is presented for the full Euler equations. This provides an example of a nonplanar structure for which the uniform Kreiss–Lopatinski–Majda stability condition can be explicitly verified.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.01.003
Nicola Costanzino 1

1 Department of Mathematics, Pennsylvania State University, University Park, PA, 16802, USA 
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Nicola Costanzino. Existence of topologically cylindrical shocks. Comptes Rendus. Mathématique, Volume 346 (2008) no. 5-6, pp. 283-286. doi : 10.1016/j.crma.2008.01.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.003/

[1] N. Costanzino, H.K. Jenssen, Multidimensional stability of shocks with geometric structure, in preparation

[2] N. Costanzino; H.K. Jenssen; G. Lyng; M. Williams Existence and stability of curved multidimensional detonation fronts, Indiana Univ. Math. J., Volume 56 (2007) no. 3, pp. 1405-1462

[3] E. Endres, H.K. Jenssen,, M. Williams, Symmetric Euler and Navier–Stokes shocks in stationary barotropic flow on a bounded domain, Preprint

[4] H.K. Jenssen; G. Lyng The Lopatinski condition for gas dynamics, Handbook of Fluid Mechanics, vol. III, North-Holland, Amsterdam, 2004, pp. 311-533 http://www.ams.org/mathscinet/search/publdoc.html?pg1=IID&s1=624956&r=9&mx-pid=2099037 appendix (pp. 507–524) to K. Zumbrun, Stability of Large-Amplitude Shock Waves of Compressible Navier–Stokes Equations

[5] A. Majda The Stability of Multi-Dimensional Shock Fronts – A New Problem for Linear Hyperbolic Equations, Mem. Amer. Math. Soc., vol. 275, Amer. Math. Soc., Providence, RI, 1983

[6] A. Majda The Existence of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., vol. 281, Amer. Math. Soc., Providence, RI, 1983

[7] G. Métivier Stability of multidimensional shocks, Advances in the Theory of Shock Waves, vol. 47, Birkhäuser, Boston, MA, 2001, pp. 25-103

[8] A. Mokrane, Problèmes mixtes hyperboliques nonlinéaires, Thèse, Université de Rennes I, 1987

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