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##
Stationary compressible fluids

In J. Serrin *Mathematical principles of classical fluid mechanics*,
In Handbuch der Physik, Bd. VIII/I, Springer-Verlag, Berlin, Göttingen,
Heidelberg, 1950. we find the following formulation of a stationary viscous
compressible barotropic fluid for the motion in
or .
:
The first of these equations corresponds to the conservation of momentum
and the second to the conservation of mass. Here
is the density of the fluid and
its velocity.
is the pressure. Mostly it is assumed to be a increasing function of .
With
we assign a external force field. The constants
and
are viscosity coefficients. Solutions could be found in papers by Valli
in the case of a bounded domain, small Mach numbers and space periodic
external force. A corresponding linearized problem is given by
Here
is a positive constant,
a constant,
and
is also a positive constant. There are existence results also in case of
high Mach numbers.

**A late reference:** J. L. Boldrini (1990) *Stationary Spatially
Periodic Compressible Flows at High Mach Number*, Rend. Sem. Mat. Univ.
Padova, Vol 84.

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collected and worked out by Wolfgang Sprößig, TU-Bergakademie
Freiberg