When a fluid is in motion, it must move in such a way that mass is conserved. To see how mass conservation places restrictions on the velocity field, consider the steady flow of fluid through a duct ...

Finite element methods (FEM) have emerged as a cornerstone in the simulation and analysis of complex fluid dynamics problems, particularly those involving curved and deformable surfaces. These ...

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.