Dispersive PDE and Interfacial Fluid Dynamics

色散偏微分方程和界面流体动力学

• 批准号: 1008387
• 负责人: David Ambrose
• 金额: $ 15.9万
• 依托单位: Drexel University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1008387&HistoricalAwards=false
• 关键词: Dispersive; PDE; Interfacial; Fluid; Dynamics

The Principal Investigator and his collaborators will address several problems in interfacial fluid dynamics and dispersive partial differential equations.The following are the specific activities to be undertaken: (A) Time-periodic interfacial fluid flows, such as water waves and vortex sheets with surface tension, will be investigated, both computationally and analytically. (B) Breakdown of smooth solutions for interfacial flows will be investigated, specifically addressing the question of whether a Moore singularity can occur for flows with surface tension. (C) Well-posedness of rotational interfacial Hele-Shaw flows will be proved. (D) Rigorous studies of the well-posedness or ill-posedness of equations with degenerate dispersion, such as the Rosenau-Hyman equations, will be performed.There are many practical situations in science and engineering which involve interfaces between moving fluids, such as the mixing of fluids in the ocean, or the motion of contaminants in groundwater. The research to be undertaken in this project will provide insight into the predictability of such motions, as well as phenomena such as wave breaking and fluid mixing. The investigator will use methods of both mathematical analysis and scientific computing as appropriate in carrying out the research. Both undergraduate and graduate students will participate in the research.

主要研究员及其合作者将解决界面流体动力学和色散偏微分方程中的几个问题，具体活动如下：（A）将从计算和分析两方面研究时间周期性界面流体流动，如水波和具有表面张力的涡面。 (B)将研究界面流的光滑解的分解，特别是解决表面张力流是否会出现摩尔奇异性的问题。 (C)证明了旋转界面Hele-Shaw流的适定性。 (D)在科学和工程中有许多实际情况涉及运动流体之间的界面，例如海洋中流体的混合，或地下水中污染物的运动。 在这个项目中进行的研究将使人们深入了解这种运动的可预测性，以及波浪破碎和流体混合等现象。 研究者将酌情使用数学分析和科学计算方法进行研究。 本科生和研究生都将参与这项研究。