We formulate, analyse and numerically simulate what are arguably the two simplest Stokes-flow free boundary problems relevant to tissue growth, extending the classical Stokes free boundary problem by incorporating (i) a volumetric source (the nutrient-rich case) and (ii) a volumetric sink, a surface source and surface compression (the nutrient-poor case). Both two- and three-dimensional cases are considered. A number of phenomena are identified and characterised thereby, most notably a buckling-associated instability in case (ii).

中文翻译：

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斯托克斯流的自由边界问题，应用于生物组织的生长

我们制定、分析和数值模拟可以说是与组织生长相关的两个最简单的斯托克斯自由边界问题，通过合并 (i) 体积源（营养丰富的情况）和（ii）扩展经典的斯托克斯自由边界问题体积汇、表面源和表面压缩（营养贫乏的情况）。考虑了二维和三维情况。许多现象由此被识别和表征，最显着的是在情况 (ii) 中与屈曲相关的不稳定性。