The Navier-Stokes Equations

The Navier-Stokes equations are fundamental mathematical formulas that describe how fluids like air and water move. They account for forces such as pressure, gravity, and viscosity (internal friction), helping predict flow patterns—like weather systems, airplane airflow, or ocean currents. These equations consider the fluid's velocity, pressure, density, and how these factors change over time and space. They are crucial for understanding and modeling complex fluid behavior in engineering, physics, and environmental science. Despite their complexity, they serve as the foundation for many applications involving fluid dynamics.