Is there a solution to Navier-Stokes?

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.

Is Navier-Stokes equation chaotic?

112. Whether turbulent solutions of the Navier–Stokes equations are chaotic is considered. Initially neighboring solutions for a low‐Reynolds‐number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time‐independent external force.

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.

What are the forces used in Navier-Stokes equation?

There are three kinds of forces important to fluid mechanics: gravity (body force), pressure forces, and viscous forces (due to friction). Gravity force, Body forces act on the entire element, rather than merely at its surfaces.

What is Incompressibility of fluid?

An incompressible fluid is defined as the fluid whose volume or density does not change with pressure. From: Advanced Reservoir Engineering, 2005.

Is turbulence a chaos?

In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between those layers.

Are Newtonian fluids incompressible?

#3. For a Newtonian fluid, viscosity depends entirely on the temperature and pressure of the liquid. Examples: Water, Air, Emulsion, Hydrogen Main Features: Newton’s Liquids have no elastic properties. They are incompressible, isotropic, and unreactive.