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arXiv · 2609.23738

On the compactness of artificial compressibility approximations of weak solutions for fluid problems in deforming domains

Stephan Schmitz·Anna Hundertmark
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Abstract

In this contribution, a fluid flow problem on a general deforming domain for a Newtonian fluid in two and three space dimensions with artificial compressibility approximation is studied. We prove an estimate on the integral equicontinuity in time of the weak solutions under suitable domain regularity assumptions, which is independent on the compressibility parameter and serves as an alternative compactness argument for the convergence of weak solution sequences for vanishing compressibility. The corresponding estimate is obtained by remapping the problem onto a fixed reference domain and using appropriate divergence-preserving testfunctions involving the difference of two solutions at different points in time, thus defined with respect to different domains/coordinates.

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Stephan Schmitz, Anna Hundertmark. 2026-09-20. On the compactness of artificial compressibility approximations of weak solutions for fluid problems in deforming domains. https://arxiv.org/abs/2609.23738

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