A generalization of the classical Euler and Korteweg fluids

Pub Date : 2023-05-29 DOI:10.21136/AM.2023.0010-23
Kumbakonam Ramamani Rajagopal
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引用次数: 2

Abstract

The aim of this short paper is threefold. First, we develop an implicit generalization of a constitutive relation introduced by Korteweg (1901) that can describe the phenomenon of capillarity. Second, using a sub-class of the constitutive relations (implicit Euler equations), we show that even in that simple situation more than one of the members of the sub-class may be able to describe one or a set of experiments one is interested in describing, and we must determine which amongst these constitutive relations is the best by culling the class by systematically comparing against an increasing set of observations. (The implicit generalization developed in this paper is not a sub-class of the implicit generalization of the Navier-Stokes fluid developed by Rajagopal (2003), (2006) or the generalization due to Průša and Rajagopal (2012), as spatial gradients of the density appear in the constitutive relation developed by Korteweg (1901).) Third, we introduce a challenging set of partial differential equations that would lead to new techniques in both analysis and numerical analysis to study such equations.

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经典欧拉流体和Korteweg流体的推广
这篇短文的目的有三个。首先,我们对Korteweg(1901)提出的本构关系进行了隐式推广,该关系可以描述毛细现象。其次,使用本构关系的一个子类(隐式欧拉方程),我们表明,即使在这种简单的情况下,该子类的不止一个成员也可能能够描述一个或一组有兴趣描述的实验,我们必须通过系统地与越来越多的观测结果进行比较来筛选类别,从而确定这些本构关系中哪一个是最好的。(本文中开发的隐式推广不是Rajagopal(2003)、(2006)开发的Navier-Stokes流体隐式推广的子类,也不是Průša和Rajagopa(2012)开发的推广,因为密度的空间梯度出现在Korteweg(1901)开发的本构关系中。)第三,我们引入了一组具有挑战性的偏微分方程,这将导致在分析和数值分析中研究此类方程的新技术。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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