论文标题
通过相对熵方法
High friction limit for Euler-Korteweg and Navier-Stokes-Korteweg models via relative entropy approach
论文作者
论文摘要
本文的目的是调查高摩擦力制度中Euler-Korteweg和Navier-Stokes-Korteweg系统的单数放松限制。我们应证明，粘度项仅在拟议的缩放率中以较高的阶段存在，因此不会影响限制动力学，并且两个模型共享相同的平衡方程。使用相对熵技术在弱的，有限的能量解的框架中进行弛豫模型的框架中的相对熵技术进行分析。在这里证明的结果利用了[6]中引入的漂移速度的模型的扩大表述，以这种方式概括了[15]中对Euler-Korteweg模型的证明。
The aim of this paper is to investigate the singular relaxation limits for the Euler-Korteweg and the Navier-Stokes-Korteweg system in the high friction regime. We shall prove that the viscosity term is present only in higher orders in the proposed scaling and therefore it does not affect the limiting dynamics, and the two models share the same equilibrium equation. The analysis of the limit is carried out using the relative entropy techniques in the framework of weak, finite energy solutions of the relaxation models converging toward smooth solutions of the equilibrium. The results proved here take advantage of the enlarged formulation of the models in terms of the drift velocity introduced in [6], generalizing in this way the ones proved in [15] for the Euler-Korteweg model.
