points 1 and 2 lie on a streamline, the fluid has constant density, the flow is steady, and there is no friction. Although these restrictions sound severe, the Bernoulli equation is very useful, ...

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. A new computer-assisted proof marks a major breakthrough in that quest.

The Navier-Stokes equations describe simple, everyday phenomena, like water flowing from a garden hose, yet they provide a million-dollar mathematical challenge. Physics contains equations that ...