不可压缩黏弹性方程的线性Rayleigh-Taylor不稳定性

Linear Rayleigh-Taylor Instability for Incompressible Viscoelastic Equations

本文研究带有弹性系数κ<κ_(c)和表面张力系数σ<σ_(c)的不可压缩黏弹性方程关于其稳态解的线性化方程的Rayleigh-Taylor不稳定性.通过研究一族修正的变分问题构造线性化方程的增长模式解,并利用其可能的最快时间增长率证明了线性化方程任意解的估计.

In this paper,we are concerned with the Rayleigh-Taylor instability of the equations obtained from linearizing the incompressible viscoelastic equations around a steadystate profile with the elasticity coefficientκ<κ_(c) and the surface tension coefficientσ<σ_(c).We prove an estimate for arbitrary solutions to the linearized equations in terms of the fastest possible growth rate for the growing mode solutions constructed by studying a family of modified variational problems.