👉 The Navier-Stokes equations are a set of nonlinear partial differential equations that describe the motion of fluid substances, such as liquids and gases. These equations express the conservation of mass, momentum, and energy within a fluid, accounting for various forces like gravity, pressure, viscosity, and external forces. They are fundamental in fluid dynamics, enabling the prediction of fluid flow behavior under different conditions, including velocity, pressure, temperature, and density changes. Solving these equations is crucial for a wide range of applications, from weather forecasting and oceanography to engineering problems involving pipelines, aircraft design, and hydraulic systems. Despite their importance, solving the Navier-Stokes equations analytically is challenging due to their complexity and nonlinearity, making numerical methods essential for practical applications.
