Describe the Navier-Stokes equations

Navier-Stokes equations govern the behavior of fluids and are fundamental to understanding phenomena like turbulence, airflow, and ocean currents. Describe the Navier-Stokes equations, including the terms representing viscosity, pressure, and acceleration, and discuss their solutions for different flow regimes. Explore applications of fluid dynamics in various fields, such as aerodynamics in aircraft design, weather prediction, and the study of blood flow in biological systems. Furthermore, discuss the challenges in solving the Navier-Stokes equations analytically and the importance of numerical simulations in understanding complex fluid behavior.