Stability of diffuse fluidic phase boundaries

在两相可压缩流体动力学的连续介质模型中，相之间的微力被表示为应力张量，该应力张量取决于序参数e的梯度。例如，在一个实施例中，相的混合比。该项目的目的在于捕捉稳定的参考配置，实现两个阶段，并包含相应的接口，如一个阶段的液滴周围的区域充满了其他阶段。除了经典的Korteweg模型，该项目将主要致力于系统的相场，以及最后，与不同的技术，尖锐的界面模型。关于Korteweg和相场模型，稳定性问题本身作为一个长期渐近的解决方案附近的参考解决方案，对于尖锐的界面模型，它涉及的有限时间持续的不连续性战线。

In continuum models for the dynamics of two-phase compressible fluids, microforces between the phases are expressed as stress tensors that depend on the gradient of an order parameter, e. g., the mixture ratio of the phases. The purpose of this project consists in capturing the stability of reference configurations that realise both phases and contain corresponding interfaces, such as a droplet of one phase surrounded by a region filled with the other phase. Besides classical Korteweg models, the project will primarily be devoted to systems with phase field, as well as finally, with different techniques, to sharp-interface models. Regarding Korteweg and phase-field models, the stability question poses itself as one on the long-time asymptotics of solutions near the reference solutions; regarding sharp-interface models it concerns the finite-time persistence of discontinuity fronts.