Summary
The Euler and the Navier-Stokes equations are the most established models in fluid dynamics. Scientists and engineers apply these equations to model various phenomena, including weather patterns, ocean currents, flows around vehicles, aircraft, and ships, as well as blood flow. Mathematicians and physicists believe that understanding the solutions to these equations can lead to an explanation for turbulence. Despite their wide range of applications, there is no theoretical guarantee that smooth solutions to these equations can exist for all time. Mathematically, proving whether smooth solution
