Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible
Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 9, 22 p.
@article{SEDP_2006-2007____A9_0,
     author = {Texier, Benjamin and Zumbrun, Kevin},
     title = {Bifurcation de {Hopf} d{\textquoteright}ondes de choc pour les \'equations de {Navier-Stokes} compressible},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique) dit aussi "S\'eminaire Goulaouic-Schwartz"},
     note = {talk:9},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2006-2007},
     language = {fr},
     url = {http://www.numdam.org/item/SEDP_2006-2007____A9_0/}
}
TY  - JOUR
AU  - Texier, Benjamin
AU  - Zumbrun, Kevin
TI  - Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible
JO  - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz"
N1  - talk:9
PY  - 2006-2007
DA  - 2006-2007///
PB  - Centre de mathématiques Laurent Schwartz, École polytechnique
UR  - http://www.numdam.org/item/SEDP_2006-2007____A9_0/
LA  - fr
ID  - SEDP_2006-2007____A9_0
ER  - 
Texier, Benjamin; Zumbrun, Kevin. Bifurcation de Hopf d’ondes de choc pour les équations de Navier-Stokes compressible. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2006-2007), Exposé no. 9, 22 p. http://www.numdam.org/item/SEDP_2006-2007____A9_0/

[BMR] A. Bourlioux, A. Majda, et V. Roytburd, Theoretical and numerical structure for unstable one-dimensional detonations. SIAM J. Appl. Math. 51 (1991) 303–343. | MR 1095022 | Zbl 0731.76076

[Er] J. J. Erpenbeck, Nonlinear theory of unstable one–dimensional detonations, Phys. Fluids 10 (1967) No. 2, 274–289. | Zbl 0158.45305

[FD] W. Fickett et W. Davis, Detonation : Theory and Experiment, Dover Press, Mineola, New York (2000).

[Gi] D. Gilbarg, The existence and limit behaviour of the one-dimensional shock layer, Amer. J. Math. 73 (1951), 256-274. | MR 44315 | Zbl 0044.21504

[KSh] S. Kawashima et Y. Shizuta, On the normal form of the symmetric hyperbolic-parabolic systems for one-dimensional gas motion, Tohoku Math. J. 40 (1988), 449-464. | MR 957056 | Zbl 0699.35171

[KS] A.R. Kasimov et D.S. Stewart, Spinning instability of gaseous detonations. J. Fluid Mech. 466 (2002), 179–203. | MR 1925152 | Zbl 1013.76034

[KuS] M. Kunze et G. Schneider, Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum, Z. Angew. Math. Phys. 55 (2004) 383-399. | MR 2061251 | Zbl 1063.35029

[LyZ1] G. Lyng et K. Zumbrun, A stability index for detonation waves in Majda’s model for reacting flow. Phys. D 194 (2004), no. 1-2, 1–29. | Zbl 1061.35018

[LyZ2] G. Lyng et K. Zumbrun, One-dimensional stability of viscous strong detonation waves. Arch. Ration. Mech. Anal. 173 (2004), no. 2, 213–277. | MR 2081031 | Zbl 1067.76041

[MaZ] C. Mascia et K. Zumbrun, Pointwise Green function bounds for shock profiles of systems with real viscosity. Arch. Ration. Mech. Anal. 169 (2003), no. 3, 177–263. | MR 2004135 | Zbl 1035.35074

[Pa] A. Pazy, Semigroups of linear operators and applications to partial differential equations. Applied Mathematical Sciences, 44, Springer-Verlag, New York-Berlin, (1983) viii+279 pp. ISBN : 0-387-90845-5. | MR 710486 | Zbl 0516.47023

[SS] B. Sandstede et A. Scheel, Hopf bifurcation from viscous shock waves, Preprint (2006).

[TZ1] B. Texier et K. Zumbrun, Relative Poincaré–Hopf bifurcation and galloping instability of traveling waves, Methods Anal. and Appl. 12 (2005), no. 4, 349–380. | MR 2258314 | Zbl 05137341

[TZ2] B. Texier et K. Zumbrun, Galloping instability of viscous shock waves, Preprint (2006), disponible à l’adresse http://www.math.jussieu.fr/~texier.

[TZ3] B. Texier et K. Zumbrun, Hopf bifurcation of viscous shock waves in compressible gas dynamics and MHD, à paraître dans Archive for Rational Mechanics and Analysis, disponible à l’adresse http://www.math.jussieu.fr/~texier.

[Z1] K. Zumbrun, Planar stability criteria for viscous shock waves of systems with real viscosity, in Hyperbolic Systems of Balance Laws, CIME School lectures notes, Lecture Notes in Mathematics 1911, Springer (2003). | MR 2348937 | Zbl 1138.35061

[Z2] K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier–Stokes equations, Handbook of Mathematical Fluid Dynamics vol.3, Elsevier (2004). | MR 2099037

[ZH] K. Zumbrun et P. Howard, Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J. 47 (1998), 741–871 ; Errata, Indiana Univ. Math. J. 51 (2002), no. 4, 1017–1021. | MR 1665788 | Zbl 0928.35018

[ZS] K. Zumbrun et D. Serre, Viscous and inviscid stability of multidimensional planar shock fronts, Indiana Univ. Math. J. 48 (1999) 937–992. | MR 1736972 | Zbl 0944.76027