Mathematical Sciences: Development of Mathematical Methods for Fluid Dynamics and Related Sciences

建议的研究项目将集中于发展渐近、严格的分析和数值方法，以研究表面波共振、障碍物上密度分层流体中的内波、弹性管中的生物流体流动、铁磁流体上的表面波以及无小参数的WKb近似。这些研究成果将可能应用于以下领域：空间科学中控制装置的设计，带振荡尾巴的山脉大气波，血管中的血液流动，以及核工程、地球物理、理论化学等领域的无参数物理问题的解决。

DMS-9424508 Shen The proposed research project will concentrate on the development of asymptotics, rigorous analysis and numerical methods for the investigation of surface wave resonance, internal waves in a density-stratified fluid over an obstacle, biological fluid flow in elastic tubes, surface waves on a ferromagnetic fluid, and WKB approximation without a small parameter. The research results to be obtained will have possible applications to the following areas: design of control devices in space science, atmospheric waves with oscillatory tails past a mountain range, blood flow in blood vessels, and solutions of physical problems without a parameter in nuclear engineering, geophysics, theoretical chemistry and others.