On the global stability of contact discontinuity for compressible Navier-Stokes equations

Feimin Huang; Huijiang Zhao

Rendiconti del Seminario Matematico della Università di Padova (2003)

  • Volume: 109, page 283-305
  • ISSN: 0041-8994

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Huang, Feimin, and Zhao, Huijiang. "On the global stability of contact discontinuity for compressible Navier-Stokes equations." Rendiconti del Seminario Matematico della Università di Padova 109 (2003): 283-305. <http://eudml.org/doc/108604>.

@article{Huang2003,
author = {Huang, Feimin, Zhao, Huijiang},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
language = {eng},
pages = {283-305},
publisher = {Seminario Matematico of the University of Padua},
title = {On the global stability of contact discontinuity for compressible Navier-Stokes equations},
url = {http://eudml.org/doc/108604},
volume = {109},
year = {2003},
}

TY - JOUR
AU - Huang, Feimin
AU - Zhao, Huijiang
TI - On the global stability of contact discontinuity for compressible Navier-Stokes equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2003
PB - Seminario Matematico of the University of Padua
VL - 109
SP - 283
EP - 305
LA - eng
UR - http://eudml.org/doc/108604
ER -

References

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  1. [1] F. V. ATKINSON - L. A. PELETIER, Similarity solutions of the nonlinear diffusion equation, Arch. rational Mech. Anal., 54 (1974), pp. 373-392. Zbl0293.35039MR344559
  2. [2] C. T. DUYN - L. A. PELETIER, A class of similarity solution of the nonlinear diffusion equation, Nonlinear Analysis, T.M.A., 1 (1977), pp. 223-233. Zbl0394.34016
  3. [3] F. HUANG - A. MATSUMURA - X. SHI, On the stability of contact discontinuity for compressible Navier-Stokes equations with free boundary, to appear in Osaka J. Math. Zbl1062.35066MR2040072
  4. [4] F. HUANG - A. MATSUMURA - X. SHI, A gas-solid free boundary problem for a compressible viscous gas, to appear in SIAM J. Math. Anal., 2003. Zbl1035.35070MR2000974
  5. [5] L. HSIAO - T. P. LIU, Nonlinear diffusive phenomena of nonlinear hyperbolic systems, Chin. Ann. Math. B, 14:4 (1993), pp. 465-480. Zbl0804.35072MR1254543
  6. [6] S. KAWASHIMA - A. MATSUMURA, Asymptotic stability of traveling wave solutions of systems for one-dimensional gas motion, Commun. Math. Phys., 101 (1985), pp. 97-127. Zbl0624.76095MR814544
  7. [7] S. KAWASHIMA - A. MATSUMURA - K. NISHIHARA, Asymptotic behavior of solutions for the equations of a viscous heat-conductive gas, Proc. Japan Acad., Ser. A, 62 (1986), pp. 249-252. Zbl0624.76097MR868811
  8. [8] T. LIU, Shock waves for compressible Navier-Stokes equations are stable, Comm. Pure Appl. Math., XXXIX (1986), pp. 565-594. Zbl0617.76069MR849424
  9. [9] T. LIU - Z. XIN, Nonlinear stability of rarefaction waves for compressible Navier-Stokes equations, Comm. Math. Phys., 118 (1988), pp. 451-465. Zbl0682.35087MR958806
  10. [10] T. P. LIU - Z. P. XIN, Pointwise decay to contact discontinuities for systems of viscous conservation laws, Asian J. Math., 1, no. 1 (1997), pp. 34-84. Zbl0928.35095MR1480990
  11. [11] A. MATSUMURA - M. MEI, Convergence to travelling fronts of solutions of the p-system with viscosity in the presence of a boundary, Arch. Rat. Mech. Anal., 146 (1999), pp. 1-22. Zbl0957.76072MR1682659
  12. [12] A. MATSUMURA - K. NISHIHARA, On the stability of traveling wave solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 2 (1985), pp. 17-25. Zbl0602.76080MR839317
  13. [13] A. MATSUMURA - K. NISHIHARA, Asymptotics toward the rarefaction wave of the solutions of a one-dimensional model system for compressible viscous gas, Japan J. Appl. Math., 3 (1986), pp. 1-13. Zbl0612.76086MR899210
  14. [14] A. MATSUMURA - K. NISHIHARA, Global stability of the rarefaction wave of a one-dimensional model system for compressible viscous gas, Commun. Math. Phys., 144 (1992), pp. 325-335. Zbl0745.76069MR1152375
  15. [15] A. MATSUMURA - K. NISHIHARA, Global asymptotics toward the rarefaction wave for solutions of viscous p-system with boundary effect, Q. Appl. Math., Vol. LVIII (2000), pp. 69-83. Zbl1157.35318MR1738558
  16. [16] Y. NIKKUNI - S. KAWASHIMA, Stability of stationary solutions to the halfspace problem for the discrete Boltzmann equation with multiple collisions, Kyushu J. Math., 54, no. 2 (2000), pp. 233-255. Zbl0965.35129MR1793167
  17. [17] K. NISHIHARA - T. YANG - H. ZHAO, Nonlinear stability of strong rarefaction waves for compressible Navier-Stokes equations, Preprint 2002. Zbl1065.35057MR2083790
  18. [18] K. NISHIHARA - H. ZHAO, Global stability of strong rarefaction waves for compressible Navier-Stokes equations with boundary effects, in preparation. 
  19. [19] T. PAN - H. X. LIU - K. NISHIHARA, Asymptotic behavior of a one-dimensional compressible viscous gas with free boundary, to appear in SIAM J. Math. Anal. Zbl1034.35075MR1951775
  20. [20] Z. P. XIN, On nonlinear stability of contact discontinuities, Proceeding of 5th international conferences on hyperbolic problems: theory, numerics and applications, edited by Glimm, etc., World Scientific, 1996, pp. 249-257. Zbl0918.35117MR1446032

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