Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
Surface tension stabilization of the Rayleigh-Taylor instability for a fluid layer in a porous medium
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DOI：
10.1016/j.anihpc.2020.04.005
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发表时间：
2020-11-01
影响因子：
1.9
通讯作者：
Scrobogna, Stefano
中科院分区：
文献类型：
--
作者：
Gancedo, Francisco;Granero-Belinchon, Rafael;Scrobogna, Stefano
本文研究了多孔介质中不可压缩流体在重力和毛细力作用下的动力学问题。主要的兴趣是在瑞利-泰勒不稳定的情况下，流体位于干燥区域的顶部的流体的稳定。这里考虑的一个重要特征是，流体层在不透水的墙之下。考虑到流体与固定边界的强相互作用，在流体特征高较小的情况下，这种物理情况已经通过薄膜近似得到了广泛的研究。在这里，而不是考虑任何简化导致渐近模型，我们处理完整的自由边界问题。我们证明，如果流体界面小于一个明确的常数，解决方案是全球的时间，它立即成为解析。特别地，流体不会在有限时间内形成液滴。我们的结果是在维纳空间的接口连同一些非标准的维纳-Sobolev各向异性空间所需的描述流体压力和速度的规律性。这些Wiener-Sobolev空间是独立的兴趣，因为它们可以在其他问题中有用。最后，让我们注意到，我们的技术不依赖于在散装流体的无旋特性，它们可以应用于其他自由边界问题。(C)2020 L'Association Publications de l'Institut Henri Poincare. Elsevier B. V.出版，保留所有权利。
This paper studies the dynamics of an incompressible fluid driven by gravity and capillarity forces in a porous medium. The main interest is the stabilization of the fluid in Rayleigh-Taylor unstable situations where the fluid lays on top of a dry region. An important feature considered here is that the layer of fluid is under an impervious wall. This physical situation has been widely study by mean of thin film approximations in the case of small characteristic high of the fluid considering its strong interaction with the fixed boundary. Here, instead of considering any simplification leading to asymptotic models, we deal with the complete free boundary problem. We prove that, if the fluid interface is smaller than an explicit constant, the solution is global in time and it becomes instantly analytic. In particular, the fluid does not form drops in finite time. Our results are stated in terms of Wiener spaces for the interface together with some non-standard Wiener-Sobolev anisotropic spaces required to describe the regularity of the fluid pressure and velocity. These Wiener-Sobolev spaces are of independent interest as they can be useful in other problems. Finally, let us remark that our techniques do not rely on the irrotational character of the fluid in the bulk and they can be applied to other free boundary problems. (C) 2020 L'Association Publications de l'Institut Henri Poincare. Published by Elsevier B.V. All rights reserved.