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Mathematical Analysis of the Water Wave Motion

水波运动的数学分析

基本信息

批准号：
1101434
负责人：
Sijue Wu
金额：
$ 42万
依托单位：
Regents of the University of Michigan - Ann Arbor
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2011
资助国家：
美国
起止时间：
2011-07-01 至 2016-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101434&HistoricalAwards=false
关键词：
Mathematical Analysis Water Wave Motion

项目摘要

This project is concerned with the motion of water waves in both two and three space dimensions. The particular mathematical problem under investigation is that of the motion of the interface separating a two- or three-dimensional, inviscid, incompressible, and irrotational fluid, under the influence of gravity, from a region of zero density, neglecting the effects of surface tension. The questions the principal investigator seeks to answer focus on the later-time behavior of surface waves in the open ocean for initially small wave disturbances. In particular, her primary objectives are (1) to identify those initial data that lead to finite time blow-up of the interface and to understand the nature of the singularities that develop in the interface and (2) to identify the largest set of initial data that lead to situations in which blow-up is avoided for all time. The principal investigator also seeks to justify rigorously the modulation approximations of the two- and three-dimensional water wave problems.Rogue waves are relatively large surface waves that are observed in deep ocean waters. Often appearing in perfectly clear weather without warning, they are blamed for the damage and inexplicable disappearance of numerous large ships and ocean liners. With the resolution of the questions under study in this project, the principal investigator hopes to provide insights into effective designs of computational and laboratory simulations of water wave motion and thereby to advance our understanding of the causes of natural phenomena associated with such waves, including the behavior of rogue waves. The analytical tools developed to carry out the research may also serve to shed new light on related problems in mathematical physics. The proposed research will involve graduate students.

该项目关注的是水波在二维和三维空间中的运动。研究中的特殊数学问题是将二维或三维、无粘性、不可压缩和无旋流体在重力的影响下与零密度区域分离的界面运动，忽略表面张力的影响。主要研究者试图回答的问题集中在开放海洋中最初的小波浪扰动的表面波的后期行为。特别是，她的主要目标是（1）确定那些初始数据，导致有限时间爆破的接口，并了解性质的奇点，在接口和（2），以确定最大的一组初始数据，导致的情况下，爆破是避免所有的时间。主要研究者还试图证明严格的调制近似的二维和三维水波problem.Rogue波是相对较大的表面波，在深海沃茨观察。它们经常在没有警告的情况下出现在晴朗的天气中，被指责为许多大型船只和远洋客轮的损坏和莫名其妙的失踪。随着该项目中研究问题的解决，首席研究员希望为水波运动的计算和实验室模拟的有效设计提供见解，从而促进我们对与此类波浪相关的自然现象的原因的理解，包括流氓波的行为。为进行研究而开发的分析工具也可能有助于揭示数学物理中相关问题的新观点。拟议的研究将涉及研究生。