👉 The Navier-Stokes equation, which is a fundamental set of equations in fluid dynamics, describes the motion of fluid substances by relating the velocity field of a fluid to its pressure, density, and external forces acting upon it. These equations express the conservation of mass (continuity equation) and momentum, capturing how fluid velocity, pressure, density, and velocity gradients interact to govern fluid flow. Despite their complexity, the Navier-Stokes equations are pivotal in modeling and predicting fluid behavior in various contexts, from atmospheric and oceanic flows to engineering applications like pipe flow and aerodynamics. Solving these equations accurately remains a significant challenge in mathematics and physics, with implications for understanding natural phenomena and designing efficient systems.
