  This article considers non-stationary incompressible linear fluid equations
in a moving domain. We demonstrate the existence and uniqueness of an
appropriate weak formulation of the problem by making use of the theory of
time-dependent Bochner spaces. It is not possible to directly apply established
evolving Hilbert space theory due to the incompressibility constraint. After we
have established the well-posedness, we derive and analyse a first order time
discretisation of the system.
