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This article considers non-stationary incompressible linear fluid equationsin a moving domain. We demonstrate the existence and uniqueness of anappropriate weak formulation of the problem by making use of the theory oftime-dependent Bochner spaces. It is not possible to directly apply establishedevolving Hilbert space theory due to the incompressibility constraint. After wehave established the well-posedness, we derive and analyse a first order timediscretisation of the system.

An evolving space framework for Oseen equations on a moving domain