Navier–Stokes regularization of multidimensional Euler shocks
C. M. I. Olivier Guès; Guy Métivier; Mark Williams; Kevin Zumbrun
Annales scientifiques de l'École Normale Supérieure (2006)
- Volume: 39, Issue: 1, page 75-175
- ISSN: 0012-9593
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topGuès, C. M. I. Olivier, et al. "Navier–Stokes regularization of multidimensional Euler shocks." Annales scientifiques de l'École Normale Supérieure 39.1 (2006): 75-175. <http://eudml.org/doc/82683>.
@article{Guès2006,
author = {Guès, C. M. I. Olivier, Métivier, Guy, Williams, Mark, Zumbrun, Kevin},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {1},
pages = {75-175},
publisher = {Elsevier},
title = {Navier–Stokes regularization of multidimensional Euler shocks},
url = {http://eudml.org/doc/82683},
volume = {39},
year = {2006},
}
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
PB - Elsevier
VL - 39
IS - 1
SP - 75
EP - 175
LA - eng
UR - http://eudml.org/doc/82683
ER -
References
top- [1] Alinhac S., Existence d'ondes de raréfaction pour des sytèmes quasi-linéaires hyperboliques multidimensionnels, Comm. Partial Differential Equations14 (1989) 173-230. Zbl0692.35063MR976971
- [2] Bony J.M., Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. Paris14 (1981) 209-246. Zbl0495.35024MR631751
- [3] Coppel W.A., Stability and Asymptotic Behavior of Differential Equations, D.C. Heath, Boston, 1965. Zbl0154.09301MR190463
- [4] Chazarain J., Piriou A., Introduction to the Theory of Linear Partial Differential Equations, North-Holland, Amsterdam, 1982. Zbl0487.35002MR678605
- [5] Erpenbeck J.J., Stability of step shocks, Phys. Fluids5 (1962) 1181-1187. Zbl0111.38403MR155515
- [6] Freistühler H., Szmolyan P., Spectral stability of small shock waves, Arch. Rat. Mech. Anal.164 (2002) 287-309. Zbl1018.35010MR1933630
- [7] Gardner R., Zumbrun K., The gap lemma and geometric criteria instability of viscous shock profiles, CPAM51 (1998) 797-855. Zbl0933.35136MR1617251
- [8] Gilbarg D., The existence and limit behavior of the one-dimensional shock layer, Amer. J. Math.73 (1951) 256-274. Zbl0044.21504MR44315
- [9] Guès O., Développements asymptotiques de solutions exactes de systèmes hyperboliques quasilinéaires, Asymp. Anal.6 (1993) 241-270. Zbl0780.35017MR1201195
- [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. Zbl1058.35163MR2114817
- [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. Zbl1073.35162MR2012648
- [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. Zbl1072.35122MR2118476
- [13] Guès O., Métivier G., Williams M., Zumbrun K., Stability of noncharacteristic boundary layers for the compressible Navier–Stokes and MHD equations, in preparation. Zbl1217.35136
- [14] Guès O., Métivier G., Williams M., Zumbrun K., Viscous boundary value problems for symmetric systems with variable multiplicities, in preparation. Zbl1138.35052
- [15] Goodman J., Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch. Rat. Mech. Anal.95 (1986) 325-344. Zbl0631.35058MR853782
- [16] Goodman J., Xin Z., Viscous limits for piecewise smooth solutions to systems of conservation laws, Arch. Rat. Mech. Anal.121 (1992) 235-265. Zbl0792.35115MR1188982
- [17] Guès O., Williams M., Curved shocks as viscous limits: a boundary problem approach, Indiana Univ. Math. J.51 (2002) 421-450. Zbl1046.35072MR1909296
- [18] Hörmander L., The Analysis of Linear Partial Differential Operators I, Springer, Berlin, 1983. Zbl1028.35001
- [19] Kreiss H.-O., Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math.23 (1970) 277-298. Zbl0193.06902MR437941
- [20] Kato T., Perturbation Theory for Linear Operators, Springer, Berlin, 1985. Zbl0148.12601MR1335452
- [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. Zbl0587.35046MR798756
- [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. Zbl0699.35171MR957056
- [24] Mascia C., Zumbrun K., Pointwise Green function bounds for shock profiles with degenerate viscosity, Arch. Rat. Mech. Anal.169 (2003) 177-263. Zbl1035.35074MR2004135
- [25] Majda A., Pego R., Stable viscosity matrices for systems of conservation laws, J. Differential Equations56 (1985) 229-262. Zbl0512.76067MR774165
- [26] Majda A., The Stability of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., vol. 275, AMS, Providence, RI, 1983. Zbl0506.76075MR683422
- [27] Majda A., The Existence of Multidimensional Shock Fronts, Mem. Amer. Math. Soc., vol. 281, AMS, Providence, RI, 1983. Zbl0517.76068MR699241
- [28] Métivier G., Stability of Multidimensional Shocks, in: Advances in the Theory of Shock Waves, Progress in Nonlinear PDE, vol. 47, Birkhäuser, Boston, 2001. Zbl1017.35075MR1842775
- [29] Métivier G., The block structure condition for symmetric hyperbolic systems, Bull. Lond. Math. Soc.32 (2000) 689-702. Zbl1073.35525MR1781581
- [30] Métivier G., Zumbrun K., Large viscous boundary layers for noncharacteristic nonlinear hyperbolic problems, Mem. Amer. Math. Soc.175 (826) (2005), vi+107 p. Zbl1074.35066MR2130346
- [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. Zbl1102.35332MR2073953
- [32] Métivier G., Zumbrun K., Hyperbolic boundary value problems for symmetric systems with variable multiplicities, J. Differential Equations211 (2005) 61-134. Zbl1073.35155MR2121110
- [33] Pego R., Stable viscosities and shock profiles for systems of conservation laws, Trans. Amer. Math. Soc.282 (1984) 749-763. Zbl0512.76068MR732117
- [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. Zbl1058.35164MR2073940
- [35] Steenrod N., The Topology of Fibre Bundles, Princeton University Press, Princeton, NJ, 1951. Zbl0054.07103MR39258
- [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. Zbl0989.35089MR1842778
- [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. Zbl1222.35156MR2099037
- [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. Zbl0944.76027MR1736972
Citations in EuDML Documents
top- Ya-Guang Wang, Mark Williams, The inviscid limit and stability of characteristic boundary layers for the compressible Navier-Stokes equations with Navier-friction boundary conditions
- Guy Métivier, Benjamin Texier, Kevin Zumbrun, Existence of quasilinear relaxation shock profiles in systems with characteristic velocities
- Guy Métivier, Stability of Noncharacteristic Viscous Boundary Layers
- Franck Sueur, Vorticity internal transition layers for the Navier-Stokes equations
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