By his 20th birthday Terence Tao had already earned a doctorate from Princeton University. Now, at the mature age of 24, Tao is using some of his $1.3 million National Science Foundation grant money to find out whether mathematicians should trust wave equations. The equations, also known as partial differential equations (PDEs) are used in physics to describe waves of light, sound and water.
Tao is especially concerned with testing notoriously difficult Navier-Stokes equations, which are used to measure the motion of fluid substances. He wants to see if the theoretical equations can behave the opposite way of what occurs in reality. In the material world, waves start large and gradually disperse and disappear. Tao is using computer algorithms to attempt to create the opposite effect, starting with still water and ending with an explosion.
If Tao and his team prove that Navier-Stokes equations break down in the real world, their discovery would change the foundations of fluid mechanics. There would be certain scenarios in which PDEs would need to be replaced or modified in order to avoid predicting a physically impossible blowup.
The initial conditions are smooth and placid, but as you run wave equations, they could spontaneously create oscillations, or rogue waves.