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arXiv · 2106.08312

An evolving space framework for Oseen equations on a moving domain

Ana Djurdjevac·Carsten Gräser·Philip J. Herbert
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Abstract

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.

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Ana Djurdjevac, Carsten Gräser, Philip J. Herbert. 2021-06-15. An evolving space framework for Oseen equations on a moving domain. https://doi.org/10.1051/m2an/2023074

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