Fluid Dynamics With Large BV Data

具有大量 BV 数据的流体动力学

• 批准号: 0507884
• 负责人: Robin Young
• 金额: $ 7.5万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0507884&HistoricalAwards=false
• 关键词: Fluid; Dynamics; Large; BV; Data

Abstract: DMS-0507884, R Young, University of MassachusettsTitle: Fluid Dynamics With Large BV Data This project is a study of systems of conservation laws, focussed on the equations of fluiddynamics in one space dimension. The main problem under consideration is the existenceand structure of solutions having large BV data. The P.I. will prove two major results:the first is the existence of solutions to the equations of isentropic gas dynamics with large data (including the vacuum), and the second is the construction of time-periodic shockless solutions of the Euler equations of gas dynamics.This project extends mature results for solutions having small data to the physically in-teresting regime of large data, and makes accessible many fundamental questions for systems with large data. These include the structure of solutions, decay, uniqueness and continuous dependence, and convergence of viscous and/or relaxation approximations. Moreover, the periodic solutions developed here contain a number of new features not previously known in hyperbolic systems, such as a group velocity, sustainability of solutions, and soliton-like traveling waves. The results of this project also raise challenging questions for numerical analysts and experimentalists.

摘要：DMS-0507884， R Young，马萨诸塞大学：基于大BV数据的流体动力学。这个项目是一个守恒定律系统的研究，重点是一维空间的流体动力学方程。考虑的主要问题是具有大BV数据的解的存在性和结构。P.I.将证明两个主要结果：第一是具有大数据（包括真空）的等熵气体动力学方程解的存在性，第二是气体动力学欧拉方程的时间周期无冲击解的构造。该项目将小数据解决方案的成熟结果扩展到物理上有趣的大数据体系，并为具有大数据的系统提供了许多基本问题。这些包括解的结构，衰减，唯一性和连续依赖性，以及粘性和/或松弛近似的收敛性。此外，这里发展的周期解包含许多以前在双曲系统中不知道的新特征，如群速度、解的可持续性和类孤子行波。该项目的结果也为数值分析和实验提出了具有挑战性的问题。