Abstract
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and t he upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces.We are concerned with the Rayleigh–Taylor instability when the upper fluid is heavier than the lower fluid along the equilibrium interface. When the surface tension at the free internal interface is below the critical value, we prove that the problem is nonlinear unstable.
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Communicated by P. Constantin
J. Jang was supported in part by NSF Grants DMS-1212142 and DMS-1351898.
Y. J. Wang was supported by the National Natural Science Foundation of China (Nos.11201389, 11531010), the Fujian Province Natural Science Funds for Distinguished Young Scholar (No. 2015J06001), a Foundation for the Author of National Excellent Doctoral Dissertation of PR China (No. 201418), the Specialized Research Fund for the Doctoral Program of Higher Education (20120121120023), Xiamen University President Fund (20720150211), and Program for New Century Excellent Talents in Fujian Province University.
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Jang, J., Tice, I. & Wang, Y. The Compressible Viscous Surface-Internal Wave Problem: Nonlinear Rayleigh–Taylor Instability. Arch Rational Mech Anal 221, 215–272 (2016). https://doi.org/10.1007/s00205-015-0960-0
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DOI: https://doi.org/10.1007/s00205-015-0960-0