Navier–Stokes equations

Article

The Navier–Stokes equations describe the motion of viscous fluids such as liquids and gases. They express conservation of momentum while incorporating pressure, viscosity, body forces, and fluid acceleration.

Together with conservation of mass and suitable equations of state or energy, they form the foundation of much of fluid dynamics. Different forms are used for compressible, incompressible, laminar, turbulent, steady, and unsteady flows.

Exact solutions exist for some simplified situations, but most practical problems require approximation, numerical simulation, or experiments. Turbulence creates especially complex interactions across many spatial and temporal scales.

The equations are applied to weather, ocean circulation, aerodynamics, pipe flow, blood flow, combustion, astrophysics, and geophysical processes. The mathematical question of whether smooth three-dimensional solutions always exist is a major unsolved problem.

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• Source / publisher: Wikipedia
• URL type: WWW
• Credits: Wikipedia
• URL: https://en.wikipedia.org/wiki/Navier–Stokes_equations