Table of Contents
- 1 What will happen if Navier-Stokes equation is solved?
- 2 Why do we need Navier-Stokes equation?
- 3 Why are the Navier-Stokes equations so difficult to solve?
- 4 Can we solve Navier Stokes equation?
- 5 Does Navier Stokes conserve energy?
- 6 Has any millennium problem been solved?
- 7 What are the other terms in the Navier-Stokes equations?
- 8 How can I derive the NSE of a given volume?
You’d be able to perfectly model complex systems such as stellar gases. You’d be able to perfectly describe fluid flow through a pipe, and reduce turbulence such that you get maximum efficiency out of transport of fluids such as oil.
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.
What does it mean to solve Navier-Stokes equation?
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.
Navier-Stokes is on the extreme end of the spectrum. The difficulty of the mathematics of the equation is, in some sense, an exact reflection of the complexity of the turbulent flows they’re supposed to be able to describe.
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.
Can Navier Stokes be solved?
The Navier-Stokes equations consists of a time-dependent continuity equation for conservation of mass, three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation.
Has any millennium problem been solved?
To date, the only Millennium Prize problem to have been solved is the Poincaré conjecture, which was solved in 2003 by the Russian mathematician Grigori Perelman.
What is Navier-Stokes’s existence and uniqueness problem?
It’s the Navier-Stokes existence and uniqueness problem, based on equations written down in the 19th century. The solution of this prize problem would have a profound impact on our understanding of the behaviour of fluids which, of course, are ubiquitous in nature.
The other terms in the Navier-Stokes equations are the density of the fluid , the pressure , the frictional shear stresses , and body forces which are forces that act throughout the entire body such as inertial and gravitational forces.
How can I derive the NSE of a given volume?
The traditional approach is to derive teh NSE by applying Newton’s law to a \\fnite volume of uid.
How do scientists and mathematicians solve fluid dynamics equations?
Until the advent of scientific computing engineers, scientists and mathematicians could really only rely on very approximate solutions. In modern computational fluid dynamics (CFD) codes the equations are solved numerically, which would be prohibitively time-consuming if done by hand.