  We prove the stability of contact discontinuities without shear, a family of
special discontinuous solutions for the three-dimensional full Euler systems,
in the class of vanishing dissipation limits of the corresponding
Navier-Stokes-Fourier system. We also show that solutions of the
Navier-Stokes-Fourier system converge to the contact discontinuity when the
initial datum converges to the contact discontinuity itself. This implies the
uniqueness of the contact discontinuity in the class that we are considering.
Our results give an answer to the open question, whether the contact
discontinuity is unique for the multi-D compressible Euler system. Our proof is
based on the relative entropy method, together with the theory of
$a$-contraction up to a shift.
