This is a preview. Log in through your library . Abstract The present article is devoted to the study of the well-posedness, blow-up criterion, and lower semicontinuity of the existence time for 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 ...

Many people find complex math puzzling, including some mathematicians. Recently, a mathematician has found solutions to a puzzle that has been around for centuries. They have found a way to generate ...

For centuries, mathematicians have tried to prove that Euler’s fluid equations can produce nonsensical answers. A new approach to machine learning has researchers betting that “blowup” is near. For ...

The Navier–Stokes partial differential equation was developed in the early 19th century by Claude-Louis Navier and George Stokes. It has proved its worth for modelling incompressible fluids 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.