The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous features of the physical world: the flow of fluids. The equations, which date to the 1820s, are today used to ...

A 115-year effort to bridge the particle and fluid descriptions of nature has led mathematicians to an unexpected answer. In 1900, the great mathematician David Hilbert presented a list of 23 unsolved ...

Two mathematicians prove that under certain extreme conditions, the Navier-Stokes equations output nonsense. The Navier-Stokes equations capture in a few succinct terms one of the most ubiquitous ...

Perhaps the oldest and most prominent of these equations, formulated by Leonhard Euler more than 250 years ago, describe the flow of an ideal, incompressible fluid: a fluid with no viscosity, or ...

Virial coefficients are fundamental parameters in the statistical description of fluids, encapsulating the effects of molecular interactions on macroscopic thermodynamic properties. Through the virial ...