Abstract
<abstract><p>In this paper, we consider the linear Rayleigh-Taylor instability of an equilibrium state of 3D gravity-driven compressible viscoelastic fluid with the elasticity coefficient $ \kappa $ is less than a critical number $ \kappa_{c} $ in a moving horizontal periodic domain. We first construct the maximal growing mode solutions to the linearized equations by studying a family of modified variational problems, and then we prove an estimate for arbitrary solutions to the linearized equations.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference25 articles.
1. S. Chandrasekhar, Hydrodynamic and hydromagnetic stability, Clarendon Press, 1961.
2. R. Duan, F. Jiang, On the Rayleigh-Taylor instability for incompressible, inviscid magnetohydrodynamic flows, SIAM J. Appl. Math., 71 (2011), 1990–2013. https://doi.org/10.1137/110830113
3. D. Ebin, Ill-posedness of the Rayleigh-Taylor and Helmholtz problems for incompressible fluids, Commun. Part. Diff. Eq., 13 (1988), 1265–1295. https://doi.org/10.1080/03605308808820576
4. G. L. Gui, Z. F. Zhang, Global stability of the compressible viscous surface waves in an infinite layer, 2022, arXiv: 2208.06654.
5. Y. Guo, I. Tice, Compressible, inviscid Rayleigh-Taylor instability, Indiana U. Math. J., 60 (2011), 677–712.