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引用次数: 0
摘要
最近的几篇论文讨论了组织生长的多相模型，其中速度与压力根据物理定律之一（Stokes’s, Brinkman’s或Darcy’s）相关。虽然这些模型中的每一个都被广泛研究过，但它们之间的联系却鲜为人知。在最近的论文（David et al. In SIAM J. Math）中。在假定压力为线性形式的前提下，作者通过一个无粘极限将两个多相模型连接起来：粘弹性模型（Brinkman型）和无粘模型（Darcy型）。在这里，我们证明对于非线性幂律压力也是如此。新的成分是我们利用压力p和布林克曼势W之间的关系从W的空间紧性推导出p在空间中的紧性。
On the Inviscid Limit Connecting Brinkman’s and Darcy’s Models of Tissue Growth with Nonlinear Pressure
Several recent papers have addressed the modelling of tissue growth by multi-phase models where the velocity is related to the pressure by one of the physical laws (Stokes’, Brinkman’s or Darcy’s). While each of these models has been extensively studied, not so much is known about the connection between them. In the recent paper (David et al. in SIAM J. Math. Anal. 56(2):2090–2114, 2024), assuming the linear form of the pressure, the Authors connected two multi-phase models by an inviscid limit: the viscoelastic one (of Brinkman’s type) and the inviscid one (of Darcy’s type). Here, we prove that the same is true for a nonlinear, power-law pressure. The new ingredient is that we use the relation between the pressure p and the Brinkman potential W to deduce compactness in space of p from the compactness in space of W.
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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