Existence and stability of compressible current-vortex sheets in three-dimensional magnetohydrodynamics

Archive for Rational Mechanics and Analysis

Volumn 187, Issue 3, 2008, Pages 369-408

  Chen, Gui Qiang ^a,b   Wang, Ya Guang ^c  

^a FUDAN UNIVERSITY   (China)

^b NORTHWESTERN UNIVERSITY   (United States)

^c SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38149084312     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-007-0070-8     Document Type: Article

References (27)

1. Alinhac S. (1989) Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Commun. Partial Differ. Eqs. 14, 173-230
2. Artola M., Majda A. (1987) Nonlinear development of instability in supersonic vortex sheets, I: The basic kink modes. Phys. D. 28, 253-281
3. Artola M., Majda A. (1989) Nonlinear development of instability in supersonic vortex sheets. II SIAM J. Appl. Math. 49, 1310-1349
4. Artola M., Majda A. (1989) Nonlinear kind modes for supersonic vortex sheets. Phys. Fluids 1A: 583-596
5. Begelman M.C., Blandford R.D., Rees M.J. (1984) Theory of exagalactic radio sources. Rev. Mod. Phys. 56, 255-351
6. Blokhin, A., Trakhinin, Y.: Stability of strong discontinuities in fluids and MHD, In: Handbook of Mathematical Fluid Dynamics. Vol. I, pp. 545-652, North-Holland, Amsterdam, 2002
7. Chen G.-Q., Feldman M. (2003) Multidimensional transonic shocks and free boundary problems for nonlinear equations of mixed type. J. Am. Math. Soc. 3, 461-494
8. Chen S. (1982) On the initial-boundary value problems for quasilinear symmetric hyperbolic systems with characteristic boundary (in Chinese). Chinese Anal. Math. 3, 222-232
9. Coulombel J.F., Secchi P. (2004) Stability of compressible vortex sheet in two space dimensions. Indiana Univ. Math. J. 53, 941-1012
10. Coulombel, J.F., Secchi, P.: Nonlinear compressible vortex sheets in two space dimensions. Preprint, 2006
11. Courant R., Friedrichs K. (1948) Supersonic Flow and Shock Waves. Springer, New York
12. Francheteau J., Métivier G. (2000) Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimensionnels. Astérisque 268, 1-198
13. Friedrichs K.O., Lax P.D. (1965) Boundary value problems for first order operators. Comm. Pure Appl. Math. 18, 355-388
14. Glimm, J., Majda, A.: Multidimensional Hyperbolic Problems and Computations, The IMA Volumes in Mathematics and its Applications, Vol. 29. Springer, New York, 1991
15. Guès O. (1990) Problème mixte hyperbolique quasi-linéaire caractéristique. Commun. Partial Differ. Eqs. 15, 595-645
16. Guès O., Métivier G., Williams M., Zumbrun K. (2005) Existence and stability of multidimensional shock fronts in the vanishing viscosity limit. Arch. Ration. Mech. Anal. 175, 151-244
17. Hörmander L. (1982) The boundary problems of physical geodesy. Arch. Ration. Mech. Anal. 62, 1-52
18. Kreiss H.-O. (1970) Initial boundary value problems of hyperbolic systems. Comm. Pure Appl. Math. 23, 277-296
19. Lions J.L., Magenes E. (1972) Non-Homogeneous Boundary Value Problems and Applications, Vol. 1-3. Springer, New York
20. Majda A. (1984) Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer, New York
21. Métivier, G.: Stability of multimensioanl shocks. In: Advances in The Theory of Shock Waves, Vol. 47, pp. 25-103. PNDEA, Birkhäuser, Boston, 2001
22. Miles J.W. (1957) On the reflection of sound at an interface of relative motion. J. Acoust. Soc. Am. 29, 226-228
23. Miles J.W. (1958) On the disturbed motion of a plane vortex sheet. J. Fluid Mech. 4, 538-552
24. Smart L.L., Norman M.L., Winkler K.A. (1984) Shocks, interfaces, and patterns in supersonic jets. Physica 12D: 83-106
25. Trakhinin Y. (2005) Existence of compressible current-vortex sheets: variable coefficients linear analysis. Arch. Ration. Mech. Anal. 177, 331-366
26. Van Dyke M. (1982) An Album of Fluid Motion. Parabolic, Stanford
27. von Neumann J. (1963) Collected Works, Vol 5. Pergamon, New York