The Euler equations constitute a fundamental set of hyperbolic partial differential equations that describe the motion of an inviscid fluid. In gas dynamics, these equations are instrumental in ...

Purdue faculty dedicate countless hours to exploring the frontiers of their respective fields, pushing the boundaries of knowledge and contributing to the ever-evolving landscape of academia. To ...

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 ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

What is it that makes Euler's identity, e]iPi + 1 = 0, so special? In Euler's Pioneering Equation Robin Wilson shows how this simple, elegant, and profound formula links together perhaps the five most ...

This video explores one of Leonhard Euler’s most elegant ideas, showing how factorials can be used to connect π, square roots, and one-half in a surprising and beautiful way. Through clear ...

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 ...