Although Navier–Stokes equations are the foundation of modern hydrodynamics, adapting them to quantum systems has so far been ...

In a preprint paper, Yu Deng, Zaher Hani, and Xiao Ma delivered a rigorous derivation of the equations of fluid mechanics, including the famous Navier-Stokes and Euler equations, starting from ...

In order to understand the Navier-Stokes equations and their derivation we need considerable mathematical training and also a sound understanding of basic physics.

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. ... The famed Navier-Stokes equations can lead to cases where more than ...

[1] Derivation of Navier–Stokes equation in rotational frame for engineering flow analysis. International Journal of Thermofluids (2021). [2] Extensions to the Navier–Stokes equations .

It’s also much more generalizable, capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining.

Mathematicians have developed many ways of trying to solve the problem. New work posted online in September raises serious questions about whether one of the main approaches pursued over the years ...

The Navier-Stokes equations describe how water flows in turbulent situations. williams_jt / Flickr A huge mathematical breakthrough might have just been made, but a language barrier is slowing ...

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