As we celebrate the International Year of Quantum Science and Technology (IYQ) in 2025, we look back on a century of quantum mechanics—a field that has fundamentally changed the way we understand ...

The Navier-Stokes equations represent a cornerstone of fluid dynamics, providing a mathematical framework to describe the motion of viscous fluids. These nonlinear partial differential equations ...

The compressible Navier-Stokes equations form the cornerstone of fluid dynamics, describing the motion of viscous compressible fluids under conservation of mass, momentum and energy. By incorporating ...

In this paper, we give a pointwise estimate of the uniform space-analyticity radius of solutions of the Navier-Stokes equation in terms of the vorticity magnitude as well as in terms of the Grashof ...

A daring speculation offers a potential way forward in one of the great unsolved problems of mathematics: the behavior of the Navier-Stokes equations for fluid flow From Quanta Magazine (find original ...

Equations are the bedrock of science, expressing how numbers or physical properties relate at a fundamental level. Without equations, most of our technology would never have been invented. We may have ...

Wind energy is a critical part of the global energy transition, and yet there is one fundamental issue that physicists and engineers have been unable to solve. Reliability is a cornerstone of ...

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 ...