Navier-Stokes Existence and Smoothness

The Navier-Stokes existence and smoothness problem is a major unsolved question in mathematics and physics. It concerns the equations that describe how fluids, like water or air, move. Specifically, it asks whether solutions to these equations always exist and if they remain smooth (without any sudden changes) over time in three-dimensional space. Proving this would enhance our understanding of fluid dynamics and has implications for various fields, including engineering and meteorology. A positive answer confirms the reliability of fluid behavior predictions, while a negative might reveal unexpected complexities in nature.