TheL2 squeezing property for nonlinear bipolar viscous fluids

A squeezing property inL2(Ω) is established for orbits of the semigroup associated with the equations of motion of a nonlinear incompressible bipolar viscous fluid; it is assumed thatΩ=[0,L] n ,n=2 or 3,L>0, and that the velocity vector satisfies a spatial periodicity condition. The proof depends, in an essential manner, on key estimates for both the nonlinear operator generated by the nonlinear viscosity term in the model and the time integral of theH3(Ω) norm of the velocity.