The Navier-Stokes equations are a set of partial differential equations that govern the behavior of fluids in motion, such as water or air. They are widely considered to be among the most challenging mathematical problems known to humanity, and remain unsolved despite decades of effort by researchers. These equations describe how fluid flows through different objects, both in nature and in human-made structures like bridges. It is worth noting that the Navier-Stokes problem is one of the seven Millennium Prize Problems, with a $1 million prize for anyone who can provide a solution by 2035. Despite ongoing efforts, a general solution to this problem has not yet been discovered.
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