  In 1983, Antontsev, Kazhikhov, and Monakhov published a proof of the
existence and uniqueness of solutions to the 3D Euler equations in which on
certain inflow boundary components fluid is forced into the domain while on
other outflow components fluid is drawn out of the domain. A key tool they used
was the linearized Euler equations in vorticity form. We extend their result on
the linearized problem to multiply connected domains and establish
compatibility conditions on the initial data that allow higher regularity
solutions.
