* Astronomy

The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. These equations establish that changes in momentum (acceleration) of fluid particles are simply the product of changes in pressure and dissipative viscous forces (similar to friction) acting inside the fluid. These viscous forces originate in molecular interactions and dictate how sticky (viscous) a fluid is. Thus, the Navier-Stokes equations are a dynamical statement of the balance of forces acting at any given region of the fluid.

Title: Immortal Smooth Solution of the Three Space Dimensional Navier-Stokes System
Authors: Penny Smith
(revised v4)

We prove the existence of a smooth solution for all time--under physicially reasonable hypothesis on the initial data--for the Navier-Stokes System in three dimensions.

to read more. (9kb, PDF)