Bipolar Isothermal Non-Newtonian Compressible Fluids

The existence and uniqueness of a solution to isothermal non-Newtonian bipolar fluid is proved. We consider a special case, where the stress tensor is expressed in the form of potentials depending on ei j and ­ ei jr­ xk.. The second part is devoted to the problem of the stability of the rest state. It is proved that the perturbations of velocity and density tend to zero in appropriate norms along a chosen time sequence. Moreover, we obtain the asymptotic stability of the rest state under the assumption of the regularity of the potential forces