new formulation for viscosity first because of the study of incompressible perfect fluids for which the following relation holds\
$$\label{incomp}
\nabla_{\mu}C^{\mu}=0.$$ The basic aim of the present paper is to investigate the dynamical role of the regulator $F$ in two relevant asymptotic regimes. On one hand, we wondered how the solution with matter creation, derived in [@BK_Bianchi] for the Bianchi I solution, depends on the causal regularization of the theory (i.e. does this effect survive in the presence of the Lichnerowicz formulation?). On the other hand, we are interested to a cosmologically relevant regime, corresponding to the flat isotropic limit, for which only the bulk viscosity must be retained (the shear viscosity being suppressed due to the isotropy hypothesis). Both these regimes are investigated via a power-law solution, which is able to capture the dominant term behavior in the asymptotic solution. Such a technique offers a satisfactory answer to the questions above and follows the original treatment in [@BK_Bianchi; @BK_Israel]. Nevertheless, the cosmological relevance of the isotropic case leads us to numerically investigate the dynamics of the system, even far from the initial singularity. A subtle point in the Lichnerowicz approach to the regularization of a viscous fluid is the 