  In [F. Jiang, S. Jiang, On instability and stability of three-dimensional
gravity driven viscous flows in a bounded domain, Adv. Math., 264 (2014)
831--863], Jiang et.al. 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,
they 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 can show the nonlinear instability result without the restrictive
condition.

Analysis of PDEs