  We consider the coupling between the equations of motion of a compressible
fluid in two and three space dimensions with Christov's equation for the heat
flux. Christov's equation is a frame indifferent formulation of the classical
model of Cattaneo that allows for the heat flux to be eliminated to obtain a
single hyperbolic equation for the temperature. The obtained system is written
in quasilinear form for the state variables density, velocity, temperature and
heat flux. It is then shown that this system is not of hyperbolic type as
consequence of the presence of the Lie-Oldroyd upper convected material
derivative involved in Christov's formulation.
