We introduce a dyadic model for the Euler equations and the Navier-Stokes equations with hyper-dissipation in three dimensions. For the dyadic Euler equations we prove finite time blow-up. In the ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

Researchers have spent centuries looking for a scenario in which the Euler fluid equations fail. Now a mathematician has finally found one. Mathematicians have suspected for years that under specific ...

The cosmos is a unique laboratory for testing the laws of physics, in particular those of Euler and Einstein. Euler described the movements of celestial objects, while Einstein described the way in ...

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.