Navier's slip and evolutionary Navier-Stokes like systems with pressure and shear-rate dependent viscosity

摘要: There is compelling experimental evidence for the viscosity of a fluid to depend on shear rate as well mean normal stress (pressure). Moreover, while can vary by several orders magnitude density suffers very minor variation, when range pressure sufficiently large, thereby providing justification considering being incompressible at same time possessing that dependent pressure. In this article we investigate mathematical properties internal unsteady three-dimensional flows such fluids subject Navier's slip boundary. We establish long-time existence weak solution large data provided depends and in suitably specified manner. This specific relationship however includes classical Navier-Stokes power law (with index r - 2, ≤ 2) special cases. Even these cases, results are presented new.