关于变形域中流体问题弱解的人工可压缩逼近的紧致性
On the compactness of artificial compressibility approximations of weak solutions for fluid problems in deforming domains
浏览论文内容
中文总结 AI 辅助
本文针对变形域上牛顿流体的人工可压缩逼近，证明了独立于可压缩参数的弱解时间积分等度连续性，为可压缩性消失时的收敛提供了替代紧致性论证。
中文摘要 AI 辅助
本文研究了一般变形域上二维和三维空间中牛顿流体的人工可压缩逼近问题。在适当的域正则性假设下，我们证明了弱解在时间上的积分等度连续性估计，该估计独立于可压缩参数，并可作为可压缩性趋于零时弱解序列收敛的替代紧致性论证。相应的估计通过将问题映射到固定参考域，并使用涉及两个不同时间点解的差值的保散度检验函数（这些函数因此定义在不同的域/坐标上）而获得。
英文摘要
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.
发表机构
- RPTU University Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道分校）
机构由 AI 辅助整理，请以论文原文为准。
