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On the compressible Navier-Stokes-Korteweg equations
On the Rayleigh-Taylor instability for the compressible non-isentropic inviscid fluids with a free interface
1. | Department of Mathematics, Shanghai Normal University, Shanghai 200234 |
2. | Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240 |
References:
[1] |
R. Duan, F. Jiang and S. Jiang, On the Rayleigh-Taylor instability for incompressible, inviscid magnetohydrodynamic flows, SIAM J. Appl. Math., 71 (2011), 1990-2013.
doi: 10.1137/110830113. |
[2] |
Y. Guo and I. Tice, Linear Rayleigh-Taylor instability for viscous, compressible fluids, SIAM J. Math. Anal., 42 (2010), 1688-1720. |
[3] |
Y. Guo and I. Tice, Compressible, inviscid Rayleigh-Taylor instability, Indiana Univ. Math. J, 60 (2011), 677-711.
doi: 10.1512/iumj.2011.60.4193. |
[4] |
H. Hwang and Y. Guo, On the dynamical Rayleigh-Taylor instability, Arch. Ration. Mech. Anal., 167 (2003), 235-253.
doi: 10.1007/s00205-003-0243-z. |
[5] |
F. Jiang and S. Jiang, On linear instability and stability of the Rayleigh-Taylor problem in magnetohydrodynamics, J. Math. Fluid Mech., 17 (2015), 639-668.
doi: 10.1007/s00021-015-0221-x. |
[6] |
F. Jiang, S. Jiang and G. Ni, Nonlinear instability for nonhomogeneous incompressible viscous fluids, Sci. China Math., 56 (2013), 665-686.
doi: 10.1007/s11425-013-4587-z. |
[7] |
J. Jang, I. Tice and Y. Wang, The compressible viscous surface-internal wave problem: Nonlinear Rayleigh-Taylor instability, Arch. Ration. Mech. Anal., 221 (2016), 215-272, arXiv:1501.07583.
doi: 10.1007/s00205-015-0960-0. |
[8] |
H. Kull, Theory of the Rayleigh-Taylor instability, Phys. Rep., 206 (1991), 197-325.
doi: 10.1016/0370-1573(91)90153-D. |
[9] |
L. Rayleigh, Analytic solutions of the Rayleigh equations for linear density profiles, Proc. London Math. Soc., 14 (1883), 170-177. |
[10] |
L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, in Scientific Paper, Cambridge University Press, Cambridge, UK, II (1990), 200-207. |
[11] |
G. I. Taylor, The instability of liquid surface when accelerated in a direction perpendicular to their planes, Proc. Roy Soc. London Ser. A, 201 (1950), 192-196.
doi: 10.1098/rspa.1950.0052. |
[12] |
Y. J. Wang and I. Tice, The viscous surface-internal wave problem: Nonlinear Rayleigh-Taylor instability, Comm. Partial Differential Equations, 37 (2012), 1967-2028.
doi: 10.1080/03605302.2012.699498. |
[13] |
Y. J. Wang, Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability, J. Math. Phys., 53 (2012), 073701, 22 pp.
doi: 10.1063/1.4731479. |
[14] |
J. Wehausen and E. Laitone, Surface waves, Handbuch der Physik, Springer-Verlag, Berlin, 9 (1960), 446-778. |
show all references
References:
[1] |
R. Duan, F. Jiang and S. Jiang, On the Rayleigh-Taylor instability for incompressible, inviscid magnetohydrodynamic flows, SIAM J. Appl. Math., 71 (2011), 1990-2013.
doi: 10.1137/110830113. |
[2] |
Y. Guo and I. Tice, Linear Rayleigh-Taylor instability for viscous, compressible fluids, SIAM J. Math. Anal., 42 (2010), 1688-1720. |
[3] |
Y. Guo and I. Tice, Compressible, inviscid Rayleigh-Taylor instability, Indiana Univ. Math. J, 60 (2011), 677-711.
doi: 10.1512/iumj.2011.60.4193. |
[4] |
H. Hwang and Y. Guo, On the dynamical Rayleigh-Taylor instability, Arch. Ration. Mech. Anal., 167 (2003), 235-253.
doi: 10.1007/s00205-003-0243-z. |
[5] |
F. Jiang and S. Jiang, On linear instability and stability of the Rayleigh-Taylor problem in magnetohydrodynamics, J. Math. Fluid Mech., 17 (2015), 639-668.
doi: 10.1007/s00021-015-0221-x. |
[6] |
F. Jiang, S. Jiang and G. Ni, Nonlinear instability for nonhomogeneous incompressible viscous fluids, Sci. China Math., 56 (2013), 665-686.
doi: 10.1007/s11425-013-4587-z. |
[7] |
J. Jang, I. Tice and Y. Wang, The compressible viscous surface-internal wave problem: Nonlinear Rayleigh-Taylor instability, Arch. Ration. Mech. Anal., 221 (2016), 215-272, arXiv:1501.07583.
doi: 10.1007/s00205-015-0960-0. |
[8] |
H. Kull, Theory of the Rayleigh-Taylor instability, Phys. Rep., 206 (1991), 197-325.
doi: 10.1016/0370-1573(91)90153-D. |
[9] |
L. Rayleigh, Analytic solutions of the Rayleigh equations for linear density profiles, Proc. London Math. Soc., 14 (1883), 170-177. |
[10] |
L. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, in Scientific Paper, Cambridge University Press, Cambridge, UK, II (1990), 200-207. |
[11] |
G. I. Taylor, The instability of liquid surface when accelerated in a direction perpendicular to their planes, Proc. Roy Soc. London Ser. A, 201 (1950), 192-196.
doi: 10.1098/rspa.1950.0052. |
[12] |
Y. J. Wang and I. Tice, The viscous surface-internal wave problem: Nonlinear Rayleigh-Taylor instability, Comm. Partial Differential Equations, 37 (2012), 1967-2028.
doi: 10.1080/03605302.2012.699498. |
[13] |
Y. J. Wang, Critical magnetic number in the magnetohydrodynamic Rayleigh-Taylor instability, J. Math. Phys., 53 (2012), 073701, 22 pp.
doi: 10.1063/1.4731479. |
[14] |
J. Wehausen and E. Laitone, Surface waves, Handbuch der Physik, Springer-Verlag, Berlin, 9 (1960), 446-778. |
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