An improved result on Rayleigh–Taylor instability of nonhomogeneous incompressible viscous flows

In [F. Jiang and S. Jiang, Adv. Math., 264, 831–863, 2014], the author and Jiang investigated the instability of Rayleigh–Taylor steady-state of a three-dimensional nonhomogeneous incompressible viscous flow driven by gravity in a bounded domain $\Omega$ of class $C^2$. In particular, we proved the steady-state is nonlinearly unstable under a restrictive condition of that the derivative function of steady density possesses a positive lower bound. In this article, by exploiting a standard energy functional and more-refined analysis of error estimates in the bootstrap argument, we further show the nonlinear instability result without the restrictive condition.

Keywords

Navier–Stokes equations, steady state solutions, Rayleigh–Taylor instability

2010 Mathematics Subject Classification

76D05, 76E09

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Published 18 May 2016