Navier–Stokes equations
The Navier–Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given how useful these equations are, mathematicians have not yet proven that in three dimensions solutions always exist, or that if they do exist, then they do not contain any bad points where they become infinite. These are called the Navier–Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics, and offered a US$1,000,000 prize (approx. €0.9M or £0.8M as of May 2022) for a solution or a counter-example.