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Navier-Stokes equations

(NS equations)
(equations that describe fluid dynamics)

The Navier-Stokes equations (NS equations) describe the motion of fluids, relating viscosity, Newton's laws and pressure. One general form:

ρ(∂v/∂t+v·∇v) = -∇p + ∇·T + f

No universally-applicable analytic solution is known so solutions are generally found through computation. For incompressible fluids, the constant density simplifies the equations somewhat.

The pluralization ("Navier-Stokes equations") may refer to the inclusion of an associated continuity equation, and possibly a form of the equation based upon energy conservation, in addition to the usual form based upon momentum conservation. Or to the fact that momentum conservation form is often broken down into three equations corresponding to the three dimensions. There are also variants of NS equations for compressible versus incompressible fluids.

These are central to hydrodynamics, and magnetohydrodynamics (MHD) uses a form that adds the forces of electromagnetism including those consequent to the fluid's flow.


(fluid mechanics,hydrodynamics,fluid dynamics)
Further reading:
https://en.wikipedia.org/wiki/Navier-Stokes_equations
https://en.wikipedia.org/wiki/Navier-Stokes_existence_and_smoothness
https://mathworld.wolfram.com/Navier-StokesEquations.html
https://www.comsol.com/multiphysics/navier-stokes-equations
https://www.grc.nasa.gov/www/k-12/airplane/nseqs.html
https://www.iit.edu/sites/default/files/2021-02/navier_stokes.pdf
https://theconversation.com/millennium-prize-the-navier-stokes-existence-and-uniqueness-problem-4244

Referenced by pages:
Darcy velocity field
general circulation model (GCM)
hydrodynamic equations
MagIC
magnetohydrodynamics (MHD)
Reynolds decomposition
viscous dissipation

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