  We consider a generalization of the compressible barotropic Navier-Stokes
equations to the case of non-Newtonian fluid in the whole space. The viscosity
tensor is assumed to be coercive with an exponent $q>1.$ We prove that if the
total mass and momentum of the system are conserved, then one can find a
constant $q_0>1$ depending on the dimension of space $n$ and the heat ratio
$\gamma$ such that for $q\in [q_0,n)$ there exists no global in time smooth
solution to the Cauchy problem. We prove also an analogous result for solutions
to equations of magnetohydrodynamic non-Newtonian fluid in 3D space.
