  We prove the existence of a unique unstable strong solution in the sense of
$L^1$-norm for an abstract Rayleigh--Taylor (RT) problem arising from
stratified viscous fluids in Lagrangian coordinates based on a bootstrap
instability method. In the proof, we develop a method to modify the initial
data of the linearized abstract RT problem based on an existence theory of
unique solution of stratified (steady) Stokes problem and an iterative
technique, so that the obtained modified initial data satisfy necessary
compatibility conditions of the (original) abstract RT problem. Applying an
inverse transformation of Lagrangian coordinates to the obtained unstable
solution, and then taking proper values of parameters, we can further get
unstable solutions for the RT problems in viscoelastic fluids,
magnetohydrodynamics (MHD) fluids with zero resistivity and pure viscous fluids
(with or without interface intension) in Eulerian coordinates. Our results can
be also extended to the corresponding inhomogeneous case (without interface).
