Mathematical Sciences: Stability and Bifurcation in Two-Layer Flows

8902166 勒纳尔迪 本文将研究系统的稳定性和分叉问题， 涉及两种不混溶流体的双层流动。 这种流动 在工业上有许多应用，例如形成 双组分纤维，输油管道，喷墨 印刷和润滑。 众所周知，这种流动可以 也表现出完全出乎意料的现象， 我们对单流体流动的认识 理论上，许多 边界的形状有可能 这两种液体。 然而，实验表明，有些形状是 比其他人更喜欢，尽管潜在的选择 机制还不太清楚。 其主要目标是 建议是研究，分析和计算， 各种稳定安排的稳定性两层 流动，以及从不稳定的安排演变出新的安排。

8902166 Renardy This proposal will study the stability and bifurcation in two-layer flows involving two immiscible fluids. Such flows have many applications in industry, such as the formation of bicomponent fibers, the transport of oil in pipelines, ink-jet printing and lubrication. It is well known that such flows can also exhibit phenomena which are totally unexpected based on our knowledge of one-fluid flows. Theoretically, many possibilities exist for the shape of the boundary separating the two fluids. Yet experiments show that some shapes are preferred over others, although the underlying selection mechanisms are not well understood. A chief objective of this proposal is to study, analytically and computationally, the stability of the various steady arrangements of two-layer flows, and the evolution of new arrangements from unstable ones.