| Issue |
ESAIM: M2AN
Volume 57, Number 5, September-October 2023
|
|
|---|---|---|
| Page(s) | 3113 - 3138 | |
| DOI | https://doi.org/10.1051/m2an/2023074 | |
| Published online | 25 October 2023 | |
An evolving space framework for Oseen equations on a moving domain
1
Freie Universität Berlin, Institut für Mathematik, Arnimallee 6, 14195 Berlin, Germany
2
Friedrich-Alexander-Universität Erlangen-Nürnberg, Department of Mathematics, Cauerstraße 11, 91058 Erlangen, Germany
3
Department of Mathematics, University of Sussex, Brighton BN1 9RF, UK
* Corresponding author: p.herbert@hw.ac.uk; p.herbert@sussex.ac.uk
Received:
24
January
2023
Accepted:
2
September
2023
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.
Mathematics Subject Classification: 35Rxx / 35K90 / 76D07 / 65M15 / 46E30 / 35R37
Key words: Evolving domain / Oseen equation / finite difference
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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