  A Pontryagin maximum principle for an optimal control problem in three
dimensional linearized compressible viscous flows is established using the
Ekeland variational principle. The controls are distributed over a bounded
domain, while the state variables are subject to a set of constraints and
governed by the linearized compressible Navier-Stokes equations. The maximum
principle is of integral-type and obtained for minimizers of a tracking-type
integral cost functional.
