Fluid Dynamics With Large BV Data

摘要：DMS-0507884，R Young，University of MassachusettsTitle：Fluid Dynamics With Large BV Data本项目是对守恒定律系统的研究，重点是一维空间中的流体动力学方程。考虑的主要问题是具有大量BV数据的解决方案的存在和结构。私家侦探将证明两个主要结果：第一个是等熵气体动力学方程在大数据（包括真空）下解的存在性，第二个是欧拉气体动力学方程的时间周期无激波解的构造，该项目将小数据下解的成熟结果推广到物理上令人感兴趣的大数据区域，并使大数据系统的许多基本问题变得容易理解。这些包括解决方案的结构，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，这里开发的周期性解决方案包含了一些新的功能，以前不知道在双曲系统，如群速度，解决方案的可持续性，和孤子类行波。这个项目的结果也提出了具有挑战性的问题，数值分析师和实验。

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.