In this presentation, we demonstrate that Hamilton's principle, which is well-known for the modeling of solids, can also be formulated to derive the Navier-Stokes equations. Furthermore, we expand Hamilton's principle to enable the introduction of ``internal variables'', which describe the space- and time-dependent evolution of the material properties. Hereby, a novel strategy for the modeling of non-Newtonian fluids is given. The presented approach inherently enables a space-time formulation, which covers different scales in the viscosity through the internal variable. The resulting system is a space-time multiscale model for complex behavior of fluid flow. Numerical examples substantiate our proposed setting by some studies from Newtonian flow to non-Newtonian regimes with fading or increasing viscosity with shear-thinning or shear-thickening behavior. Besides analyses of the physical behavior, the numerical performance of the nonlinear solvers will be analyzed, too.