Nonlinear higher-order hydrodynamics: Fluids under driven flow and shear pressure

In the context of a nonequilibrium statistical thermodynamics, based on ensemble formalism, generalized hydrodynamics fluids under driven flow and shear stress is derived. At thermodynamic level, equations state are derived, which coupled to evolution basic variables that describe hydrodynamic motion in such system. Generalized diffusion-advection Maxwell-Cattaneo advection obtained appropriate limiting situations. This nonlinear higher-order applied, an illustration, case dilute solution Brownian particles conditions flowing solvent acting as thermal bath. done framework but truncated up second order.