Then nature can, as all fluid mechanists already do, come to delight in the equations handed down to us by Claude-Louis Navier and George Gabriel Stokes.

The study of free boundary problems in the Navier-Stokes equations addresses the subtle interplay between the dynamics of viscous, incompressible fluids and the evolution of interfaces whose ...

Terence Tao, Finite time blowup for an averaged three-dimensional Navier-Stokes equation, Journal of the American Mathematical Society, Vol. 29, No. 3 (July 2016), pp. 601-674 ...

Mathematics of Computation, Vol. 57, No. 195 (Jul., 1991), pp. 123-151 (29 pages) We examine certain analytic and numerical aspects of optimal control problems for the stationary Navier-Stokes ...

Experts approached this problem by attempting to mathematically translate the Boltzmann equation, which describes a gas as microscopic particles bouncing around at a range of speeds, into the ...

New Scientist reports that Kazakh mathematician Mukhtarbay Otelbayev may have solved an extremely difficult and useful mathematics problem: the Navier-Stokes equations. This is one of the Clay ...

Yet, despite all this progress, one of the biggest unsolved mysteries in physics and mathematics remains—the Navier-Stokes equation.

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.

We use the Navier-Stokes equations every day, for applications from building rockets to designing drugs. But sometimes they break – and we don’t know why ...