  We consider the plasma-vacuum interface problem in a classical statement when
in the plasma region the flow is governed by the equations of ideal
compressible magnetohydrodynamics, while in the vacuum region the magnetic
field obeys the div-curl system of pre-Maxwell dynamics. The local-in-time
existence and uniqueness of the solution to this problem in suitable
anisotropic Sobolev spaces was proved in [P. Secchi, Y. Trakhinin, Nonlinearity
27 (2014), 105-169], provided that at each point of the initial interface the
plasma density is strictly positive and the magnetic fields on either side of
the interface are not collinear. The non-collinearity condition appears as the
requirement that the symbol associated to the interface is elliptic. We now
consider the case when this symbol is not elliptic and study the linearized
problem, provided that the unperturbed plasma and vacuum non-zero magnetic
fields are collinear on the interface. We prove a basic a priori $L^2$ estimate
for this problem under the (generalized) Rayleigh-Taylor sign condition
$[\partial q/\partial N]<0$ on the jump of the normal derivative of the
unperturbed total pressure satisfied at each point of the interface. By
constructing an Hadamard-type ill-posedness example for the frozen coefficients
linearized problem we show that the simultaneous failure of the
non-collinearity condition and the Rayleigh-Taylor sign condition leads to
Rayleigh-Taylor instability.
