Navier-Stokes
equations are partial differential equations
that describe motions of fluids (liquids
and gases). In addition to airflow analysis
for airplanes, they are useful for modeling
weather, ocean currents and many other
systems. A simplified form of these
equations within a Cartesian frame of
reference is as follows:

These equations
establish the relations among the fluxes
of the variables of interest. By solving
these equations, you can describe the
motion of fluid substances such as liquids
and gases.

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