Stabilité des chocs pour la MHD
Guy Métivier[1]
- [1] MAB Université de Bordeaux I, 33405 Talence Cedex , France ; metivier@math.u-bordeaux.fr
Séminaire Équations aux dérivées partielles (2004-2005)
- page 1-19
Access Full Article
topHow to cite
topMétivier, Guy. "Stabilité des chocs pour la MHD." Séminaire Équations aux dérivées partielles (2004-2005): 1-19. <http://eudml.org/doc/11099>.
@article{Métivier2004-2005,
affiliation = {MAB Université de Bordeaux I, 33405 Talence Cedex , France ; metivier@math.u-bordeaux.fr},
author = {Métivier, Guy},
journal = {Séminaire Équations aux dérivées partielles},
language = {fre},
pages = {1-19},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Stabilité des chocs pour la MHD},
url = {http://eudml.org/doc/11099},
year = {2004-2005},
}
TY - JOUR
AU - Métivier, Guy
TI - Stabilité des chocs pour la MHD
JO - Séminaire Équations aux dérivées partielles
PY - 2004-2005
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 19
LA - fre
UR - http://eudml.org/doc/11099
ER -
References
top- S.Bianchini, A.Bressan, Vanishing viscosity limit solutions to nonlinear hyperbolic systems, Ann. of Maths., à paraître. Zbl1082.35095
- A.M. Blokhin, Strong discontinuities in magnetohydrodynamics. Translated by A. V. Zakharov. Nova Science Publishers, Inc., Commack, NY, 1994. x+150 pp. Zbl0920.76001MR1406089
- A. Blokhin and Y. Trakhinin, Stability of strong discontinuities in fluids and MHD. in Handbook of mathematical fluid dynamics, Vol. I, 545–652, North-Holland, Amsterdam, 2002. Zbl1231.76344MR1942469
- A.M. Blokhin and Y. Trakhinin, Stability of fast parallel MHD shock waves in polytropic gas. Eur. J. Mech. B Fluids 18 (1999), 197–211. Zbl0940.76019MR1681896
- A.M. Blokhin and Y. Trakhinin, Stability of fast parallel and transversal MHD shock waves in plasma with pressure anisotropy. Acta Mech. 135 (1999), 57–71. Zbl0930.76033MR1683806
- A.M. Blokhin and Y. Trakhinin, Hyperbolic initial-boundary value problems on the stability of strong discontinuities in continuum mechanics. Hyperbolic problems : theory, numerics, applications, Vol. I (Zürich, 1998), 77–86, Internat. Ser. Numer. Math., 129, Birkhäuser, Basel, 1999. Zbl0933.35138MR1715735
- A.M. Blokhin, Y. Trakhinin, and I.Z. Merazhov, On the stability of shock waves in a continuum with bulk charge. (Russian) Prikl. Mekh. Tekhn. Fiz. 39 (1998) 29–39 ; translation in J. Appl. Mech. Tech. Phys. 39 (1998) 184–193. Zbl0921.76195MR1663879
- A.M. Blokhin, Y. Trakhinin, and I.Z. Merazhov, Investigation on stability of electrohydrodynamic shock waves. Matematiche (Catania) 52 (1997) 87–114. Zbl0907.76033MR1624964
- J. Chazarain-A. Piriou, Introduction to the theory of linear partial differential equations, Translated from the French. Studies in Mathematics and its Applications, 14. North-Holland Publishing Co., Amsterdam-New York, 1982. xiv+559 pp. Zbl0487.35002MR678605
- H. Freistühler and P. Szmolyan, Spectral stability of small shock waves. Arch. Ration. Mech. Anal. 164 (2002) 287–309. Zbl1018.35010MR1933630
- K.O. Friedrichs, Symmetric hyperbolic linear differential equations. Comm. Pure and Appl. Math. 7 (1954) 345–392. Zbl0059.08902MR62932
- K.O. Friedrichs, On the laws of relativistic electro-magneto-fluid dynamics. Comm. Pure and Appl. Math. 27 (1974) 749–808. Zbl0308.76075MR375928
- K.O. Friedrichs, P. Lax, Systems of conservation equations with a convex extension. Proc. nat. Acad. Sci. USA 68 (1971) 1686–1688. Zbl0229.35061MR285799
- C.S. Gardner, M.D. Kruskal, Stability of plane magnetohydrodynamic shocks. Phys. Fluids 7 (1964) 700–706. Zbl0121.21107MR170581
- R. Gardner, K.Zumbrun, The gap lemma and geometric criteria for instability of viscous shock profiles, Comm. Pure and Appl. Math., 51 (1998), 797–855. Zbl0933.35136MR1617251
- J.Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws, Arch.Rat.Mech.Anal., 95 (1986), pp 325–344. Zbl0631.35058MR853782
- O. Gues, G. Métivier, M. Williams, K. Zumbrun, Multidimensional viscous shocks I : degenerate symmetrizers and long time stability. J. A.M.S., à paraître. Zbl1058.35163
- O. Gues, G. Métivier, M. Williams, K. Zumbrun, Multidimensional viscous shocks II : the small viscosity limit., Comm. Pure and Appl. Math., 57 (2004) 141–218. Zbl1073.35162MR2012648
- O. Gues, G. Métivier, M. Williams, K. Zumbrun, A new approach to stability of multidimensional viscous shocks, Arch. Rat.Mech. Anal., à paraître. Zbl1058.35163
- O. Gues, G. Métivier, M. Williams, K. Zumbrun, Navier–Stokes regularization of multidimensional Euler shocks, en préparation. Zbl1173.35082
- O. Gues, G. Métivier, M. Williams, K. Zumbrun, Viscous Boundary Value Problems for Symmetric Systems with Variable Multiplicities, en préparation. Zbl1138.35052
- Guès, O., Williams, M., Curved shocks as viscous limits : a boundary problem appraoch, Indiana Univ.Math.J., 51 (2002) 421–450. Zbl1046.35072MR1909296
- J.Humphrey, K.Zumbrun, Spectral stability of small amplitude shock profiles for dissipative symmetric hyperbolic-parabolic systems, Z.Angew.Math.Phys., 53 (2002), pp 20–34. Zbl1006.35065MR1889177
- H.O. Kreiss, Initial boundary value problems for hyperbolic systems, Comm. Pure Appl. Math. 23 (1970) 277-298. Zbl0193.06902MR437941
- P. Lax, Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, CBSM-NSF Regional Conf. Ser. in Appl. Math., 11, SIAM , Philadelphia (1973). Zbl0268.35062MR350216
- A. Majda, The stability of multi-dimensional shock fronts . Mem. Amer. Math. Soc. 275 (1983). Zbl0506.76075MR683422
- A. Majda, The esistence of multi-dimensional shock fronts . Mem. Amer. Math. Soc. 281 (1983). Zbl0517.76068
- A. Majda, S. Osher, Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary, Comm. Pure Appl. Math. 28 (1975) 607-676. Zbl0314.35061MR410107
- C. Mascia, K. Zumbrun, Stability of small-amplitude shock profiles for dissipative symmetric hyperbolic–parabolic systems. Comm. Pure and Appl.Math., 57 (2004) 141–218. Zbl1060.35111MR2044067
- C. Mascia, K. Zumbrun, Stability of large-amplitude shock profiles of hyperbolic–parabolic systems. Arch. Rational Mech. Anal., 172 (2004) 93–131. Zbl1058.35160MR2048568
- G. Métivier, Stability of multidimensional weak shocks, Comm., Partial Diff. Eq., 15 (1990), 983-1028. Zbl0711.35078MR1070236
- G. Métivier, Stability of multidimensional shocks. Advances in the theory of shock waves, 25–103, Progr. Nonlinear Differential Equations Appl., 47, Birkhäuser Boston, Boston, MA, 2001. Zbl1017.35075MR1842775
- G.Métivier. The Block Structure Condition for Symmetric Hyperbolic Problems, Bull. London Math.Soc., 32 (2000), 689–702 Zbl1073.35525MR1781581
- G.Métivier, K.Zumbrun, Viscous Boundary Layers for Noncharacteristic Nonlinear Hyperbolic Problems, Memoirs of the AMS, paratre. Zbl1074.35066
- G.Métivier, K.Zumbrun, Symmetrizers and continuity of stable subspaces for parabolic–hyperbolic boundary value problems, J. Discrete. Cont. Dyn. Systems, 11 (2004) 205–220. Zbl1102.35332MR2073953
- G.Métivier, K.Zumbrun, Hyperbolic Boundary Value Problems for Symmetric Systems with Variable Multiplicities, J.Diff. Eq., paratre. Zbl1073.35155
- R. Plaza, K. Zumbrun, An Evans function approach to spectral stability of small-amplitude viscous shock profiles, Discrete and Cont. Dyn. Syst. Ser B, 10 (2004) 885–924. Zbl1058.35164MR2073940
- J.V. Ralston, Note on a paper of Kreiss, Comm. Pure Appl. Math. 24 (1971) 759–762. Zbl0215.16802MR606239
- J.Rauch, Symmetric positive systems with boundary characteristic of constant multiplicity, Trans. Amer.Math.Soc, 291 (1985), 167–185. Zbl0549.35099MR797053
- R. Sakamoto, Mixed problems for hpyerbolic equations, I, II, J. Math. Kyoto Univ. 10 (1970), 349-373 and 403-417. Zbl0203.10001
- R. Sakamoto, Hyperbolic boundary value problems, Cambridge U. P., 1982. Zbl0494.35002MR666700
- K. Zumbrun, Multidimensional stability of planar viscous shock waves. Advances in the theory of shock waves, 307–516, Progr. Nonlinear Differential Equations Appl., 47, Birkhäuser Boston, Boston, MA, 2001. Zbl0989.35089MR1842778
- K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier–Stokes equations. For Handbook of Fluid Mechanics III, S.Friedlander, D.Serre ed., Elsevier North Holland 2004. Zbl1222.35156MR2099037
- K. Zumbrun, Planar stability criteria for viscous shock waves of systems with real viscosity. Lecture notes for CIME summer school at Cetraro, 2003, preprint. MR2348937
- K.Zumbrun, P.Howard, Pointwide semigroup methods and stability of viscous shock waves, Indiana J.Math., 47 (1998), 741-871, and Indiana J.Math, 51 2002, 1017-1021. Zbl0928.35018MR1665788
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.