no. 1
Navier-Stokes regularization of multidimensional Euler shocks
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 1, pp. 75-175 
@article{ASENS_2006_4_39_1_75_0,
     author = {Gu\`es, C. M. I. Olivier and M\'etivier, Guy and Williams, Mark and Zumbrun, Kevin},
     title = {Navier-Stokes regularization of multidimensional {Euler} shocks},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {75--175},
     year = {2006},
     publisher = {Elsevier},
     volume = {Ser. 4, 39},
     number = {1},
     doi = {10.1016/j.ansens.2005.12.002},
     zbl = {05037727},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.ansens.2005.12.002/}
}
TY  - JOUR
AU  - Guès, C. M. I. Olivier
AU  - Métivier, Guy
AU  - Williams, Mark
AU  - Zumbrun, Kevin
TI  - Navier-Stokes regularization of multidimensional Euler shocks
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 2006
SP  - 75
EP  - 175
VL  - 39
IS  - 1
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.ansens.2005.12.002/
DO  - 10.1016/j.ansens.2005.12.002
LA  - en
ID  - ASENS_2006_4_39_1_75_0
ER  - 
%0 Journal Article
%A Guès, C. M. I. Olivier
%A Métivier, Guy
%A Williams, Mark
%A Zumbrun, Kevin
%T Navier-Stokes regularization of multidimensional Euler shocks
%J Annales scientifiques de l'École Normale Supérieure
%D 2006
%P 75-175
%V 39
%N 1
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.ansens.2005.12.002/
%R 10.1016/j.ansens.2005.12.002
%G en
%F ASENS_2006_4_39_1_75_0
Guès, C. M. I. Olivier; Métivier, Guy; Williams, Mark; Zumbrun, Kevin. Navier-Stokes regularization of multidimensional Euler shocks. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 39 (2006) no. 1, pp. 75-175. doi: 10.1016/j.ansens.2005.12.002

[1] Alinhac S., Existence d'ondes de raréfaction pour des sytèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations 14 (1989) 173-230. | Zbl | MR

[2] Bony J.M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. Paris 14 (1981) 209-246. | Zbl | MR | Numdam

[3] Coppel W.A., Stability and Asymptotic Behavior of Differential Equations, D.C. Heath, Boston, 1965. | Zbl | MR

[4] Chazarain J., Piriou A., Introduction to the Theory of Linear Partial Differential Equations, North-Holland, Amsterdam, 1982. | Zbl | MR

[5] Erpenbeck J.J., Stability of step shocks, Phys. Fluids 5 (1962) 1181-1187. | Zbl | MR

[6] Freistühler H., Szmolyan P., Spectral stability of small shock waves, Arch. Rat. Mech. Anal. 164 (2002) 287-309. | Zbl | MR

[7] Gardner R., Zumbrun K., The gap lemma and geometric criteria instability of viscous shock profiles, CPAM 51 (1998) 797-855. | Zbl | MR

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

[9] Guès O., Développements asymptotiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymp. Anal. 6 (1993) 241-270. | Zbl | MR

[10] Guès O., Métivier G., Williams M., Zumbrun K., Multidimensional viscous shocks I: degenerate symmetrizers and long time stability, J. Amer. Math. Soc. 18 (2005) 61-120. | Zbl | MR

[11] Guès O., Métivier G., Williams M., Zumbrun K., Multidimensional viscous shocks II: the small viscosity problem, Comm. Pure Appl. Math. 57 (2004) 141-218. | Zbl | MR

[12] Guès O., Métivier G., Williams M., Zumbrun K., Existence and stability of multidimensional shock fronts in the vanishing viscosity limit, Arch. Rat. Mech. Anal. 175 (2004) 151-244. | Zbl | MR

[13] Guès O., Métivier G., Williams M., Zumbrun K., Stability of noncharacteristic boundary layers for the compressible Navier-Stokes and MHD equations, in preparation.

[14] Guès O., Métivier G., Williams M., Zumbrun K., Viscous boundary value problems for symmetric systems with variable multiplicities, in preparation.

[15] Goodman J., Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rat. Mech. Anal. 95 (1986) 325-344. | Zbl | MR

[16] Goodman J., Xin Z., Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rat. Mech. Anal. 121 (1992) 235-265. | Zbl | MR

[17] Guès O., Williams M., Curved shocks as viscous limits: a boundary problem approach, Indiana Univ. Math. J. 51 (2002) 421-450. | Zbl | MR

[18] Hörmander L., The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983. | Zbl

[19] Kreiss H.-O., Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970) 277-298. | Zbl | MR

[20] Kato T., Perturbation Theory for Linear Operators, Springer, Berlin, 1985. | Zbl | MR

[21] Kawashima S., Systems of hyperbolic-parabolic type with applications to the equations of magnetohydrodynamics, PhD thesis, Kyoto University, 1983.

[22] Kawashima S., Shizuta Y., Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275. | Zbl | MR

[23] Kawashima S., Shizuta Y., On the normal form of the symmetric hyperbolic-parabolic systems associated with the conservation laws, Tohoku Math. J. (1988) 449-464. | Zbl | MR

[24] Mascia C., Zumbrun K., Pointwise Green function bounds for shock profiles with degenerate viscosity, Arch. Rat. Mech. Anal. 169 (2003) 177-263. | Zbl | MR

[25] Majda A., Pego R., Stable viscosity matrices for systems of conservation laws, J. Differential Equations 56 (1985) 229-262. | Zbl | MR

[26] Majda A., The Stability of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., vol. 275, AMS, Providence, RI, 1983. | Zbl | MR

[27] Majda A., The Existence of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., vol. 281, AMS, Providence, RI, 1983. | Zbl | MR

[28] Métivier G., Stability of Multidimensional Shocks, in: Advances in the Theory of Shock Waves, Progress in Nonlinear PDE, vol. 47, Birkhäuser, Boston, 2001. | Zbl | MR

[29] Métivier G., The block structure condition for symmetric hyperbolic systems, Bull. Lond. Math. Soc. 32 (2000) 689-702. | Zbl | MR

[30] Métivier G., Zumbrun K., Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems, Mem. Amer. Math. Soc. 175 (826) (2005), vi+107 p. | Zbl | MR

[31] Métivier G., Zumbrun K., Symmetrizers and continuity of stable subspaces for parabolic-hyperbolic boundary value problems, Disc. Cont. Dyn. Syst. 11 (2004) 205-220. | Zbl | MR

[32] Métivier G., Zumbrun K., Hyperbolic boundary value problems for symmetric systems with variable multiplicities, J. Differential Equations 211 (2005) 61-134. | Zbl | MR

[33] Pego R., Stable viscosities and shock profiles for systems of conservation laws, Trans. Amer. Math. Soc. 282 (1984) 749-763. | Zbl | MR

[34] Plaza R., Zumbrun K., An Evans function approach to spectral stability of small-amplitude shock profiles, J. Disc. Cont. Dyn. Syst. 10 (2004) 885-924. | Zbl | MR

[35] Steenrod N., The Topology of Fibre Bundles, Princeton University Press, Princeton, NJ, 1951. | Zbl | MR

[36] Zumbrun K., Multidimensional stability of planar viscous shock waves, in: Advances in the Theory of Shock Waves, Progress in Nonlinear PDE, vol. 47, Birkhäuser, Boston, 2001, pp. 304-516. | Zbl | MR

[37] Zumbrun K., Stability of large-amplitude shock waves of compressible Navier-Stokes equations, with an appendix by H.K. Jenssen and G. Lyng, in: Handbook of Mathematical Fluid Dynamics, vol. 3, North-Holland, Amsterdam, 2004, pp. 311-533. | MR

[38] Zumbrun K., Planar stability criteria for viscous shock waves of systems with real viscosity, in: Hyperbolic Systems of Balance Laws, Springer Lecture Notes, 2006, in press.

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

Cité par Sources :