Has anyone solved the Navier-Stokes equation?

Has anyone solved the Navier-Stokes equation?

Even more basic (and seemingly intuitive) 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 neither proved that smooth solutions always exist, nor found any counter-examples.

What does the Navier-Stokes equation represent?

The Navier-Stokes equations represent the conservation of momentum, while the continuity equation represents the conservation of mass.

Why is Navier-Stokes equation unsolvable?

The Navier-Stokes equation is difficult to solve because it is nonlinear. This word is thrown around quite a bit, but here it means something specific. You can build up a complicated solution to a linear equation by adding up many simple solutions.

Does Navier-Stokes conserve energy?

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.

Is Diane Adler Real?

Diane Adler was an American editor. She is known for editing the feature film The Presidio (1988), and for her work as an editor on the 1970s James Garner television series The Rockford Files. Adler began her career editing commercials into television shows at 20th Century Fox Television.

What are the assumptions of Navier-Stokes equation?

The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum, in other words is not made up of discrete particles but rather a continuous substance.

Why is the Navier Stokes problem difficult to solve?

The Navier Stokes equation is so hard to solve because it is non-linear. If the inertial terms were not present (either because of the geometry or because the inertial terms are negligible0, it would (and can) be much easier to solve.

Does CFD use Navier-Stokes?

1.1. To solve this problem, we should know the physical properties of fluid by using Fluid Mechanics. Then we can use mathematical equations to describe these physical properties. This is Navier-Stokes Equation and it is the governing equation of CFD.

Are Navier-Stokes equations parabolic?

The Navier-Stokes equations are the fundamental equations governing the motion of viscous fluid. Among the versions of these equations, we consider here the nonstationary Navier-Stokes equations for viscous incompressible fluid. The system of equations is a nonlinear parabolic equation.

How did Mary solved 57 multiplied by 135?

Imagine that your 7-year-old could multiply 57 X 135 in her head, and tell her elementary school teacher the correct answer was 7,695. And then volunteer that the square root of that sum was 87.7 “and change.”