Navier-Stokes equations describe fluid motion in differential form, analogous to Newton's second law (F=ma). Their complexity arises from being non-linear differential equations, where the solution at any point depends on conditions throughout the fluid and its history. These equations couple mass, momentum, and energy, requiring simultaneous solutions under normal circumstances. In specific flow scenarios, such as supersonic flow, they transform into hyperbolic partial differential equations, allowing for reduced complexity based on upstream conditions. The dependence on past instants is due to the finite speed of information transfer within the fluid.