## What does the Navier-Stokes equation calculate?

Navier-Stokes equation, in fluid mechanics, a partial differential equation that describes the flow of incompressible fluids. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.

## Has anyone ever solved the Navier-Stokes equation?

In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Even more basic (and seemingly intuitive) properties of the solutions to Navier–Stokes have never been proven.

**Is Navier-Stokes equation unsteady equation?**

Navier-Stokes Equations. On this slide we show the three-dimensional unsteady form of the Navier-Stokes Equations. These equations describe how the velocity, pressure, temperature, and density of a moving fluid are related. The equations were derived independently by G.G.

**Why is Navier-Stokes equation used?**

The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing.

### How many unknowns in Navier-Stokes equations are there?

1.8 Navier-Stokes equations

Number of Equations | Number of Unknowns | |
---|---|---|

continuity | 1 | 1 |

Navier-Stokes | 3 (symmetry) | 3 |

4 | 4 |

### What is Navier Stokes equation in CFD?

From CFD-Wiki The Navier-Stokes equations are the basic governing equations for a viscous, heat conducting fluid. It is a vector equation obtained by applying Newton’s Law of Motion to a fluid element and is also called the momentum equation.

**Is Navier-Stokes equation well posed?**

It is known that the Navier-Stokes equation is globally well-posed for small data in BMO^{-1}.