Can the Navier-Stokes equations be solved?

Can the Navier-Stokes equations be solved?

Even more basic properties of the solutions to Navier–Stokes have never been proven. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proved that smooth solutions always exist. This is called the Navier–Stokes existence and smoothness problem.

Who proved 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.

Is Navier Stokes equation elliptic?

At steady-state, the Navier-Stokes equations are elliptic. In Elliptic problems, the boundary conditions must be applied on all confining surfaces.

What's the hardest math equation?

But those itching for their Good Will Hunting moment, the Guinness Book of Records puts Goldbach's Conjecture as the current longest-standing maths problem, which has been around for 257 years. It states that every even number is the sum of two prime numbers: for example, 53 + . So far so simple.

Why is Navier Stokes important?

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.

Is Navier Stokes proven?

There is no proof, since they are not a mathematical fact. Navier-Stokes equations are a model for streaming fluids, one that engineers and physicists take as the best theoretical model for their object of study (according to what I know).

What are the 7 hardest math problems?

The problems are the Birch and Swinnerton-Dyer conjecture, Hodge conjecture, Navier–Stokes existence and smoothness, P versus NP problem, Poincaré conjecture, Riemann hypothesis, and Yang–Mills existence and mass gap.

Why is Navier-Stokes non linear?

The nonlinear term in Navier–Stokes equations of Equation (1.17) is the convection term, and most of the numerical difficulties and stability issues for fluid flow are caused by this term. ... For the fluid flow with a high Reynolds number, the flow can be turbulence with multiscale responses.

What is the use of Navier-Stokes equation?

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.

Which country has toughest maths?

But when it comes to having the hardest math, China and South Korea top the list.

What is the solution to the Navier Stokes existence and smoothness problem?

The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space.

How is the jet related to the Navier Stokes problem?

The jet exhibits a wide range of length scales, an important characteristic of turbulent flows. The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space.

Can a computer solve the Navier Stokes equation?

It’s also much more generalizable, capable of solving entire families of PDEs—such as the Navier-Stokes equation for any type of fluid—without needing retraining.

When did Diane Adler solve the Navier Stokes problem?

Since understanding the Navier–Stokes equations is considered to be the first step to understanding the elusive phenomenon of turbulence, the Clay Mathematics Institute in May 2000 made this problem one of its seven Millennium Prize problems in mathematics.