Mathematical equations describing flowing water may contain points where fluid velocity becomes infinite

Physicists and mathematicians have used the Navier-Stokes equations since the 1840s to describe fluid flow, yet it is unknown if smooth solutions always exist in three dimensions. The 'smoothness' problem asks whether a fluid can develop a singularity—a point where the velocity or pressure becomes infinite—starting from perfectly normal conditions. While 2D flows are proven to be stable, the 3D version remains a Millennium Prize challenge.