An evolving space framework for Oseen equations on a moving domain

TL;DR

This paper develops a mathematical framework for analyzing the Oseen equations in moving domains, establishing well-posedness and proposing a time discretization method for non-stationary incompressible fluid flow.

Contribution

It introduces an evolving space approach for the Oseen equations on moving domains, addressing the incompressibility constraint and providing a basis for numerical methods.

Findings

Proved existence and uniqueness of weak solutions.

Developed a first order time discretization scheme.

Analyzed the stability and convergence of the discretization.

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.