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 weather, design better airplanes, and characterize how blood flows through the circulatory system. Perhaps the oldest and most prominent of these equations, formulated by Leonhard Euler more than 250 years ago, describe the flow of an ideal, incompressible fluid: a fluid with no viscosity, or internal friction, and that cannot be forced into a smaller volume. Mathematicians have long suspected that there exist initial conditions that cause the equations to break down. But they haven’t been able to prove it. In a preprint posted online in October, a pair of mathematicians has shown that a particular version of the Euler equations does indeed sometimes fail. Rafael de la Llave, a professor in the School of Mathematics who studies dynamical systems and mathematical physics, comments on the findings.
A New Computer Proof ‘Blows Up’ Centuries-Old Fluid Equations