项目名称: 完全可压Navier-Stokes方程流入问题强粘性接触间断波的渐近稳定性
项目编号: No.11426062
项目类型: 专项基金项目
立项/批准年度: 2015
项目学科: 数理科学和化学
项目作者: 郑婷婷
作者单位: 福建农林大学
项目金额: 3万元
中文摘要: Navier-Stokes方程是流体力学中重要的数学模型之一,但是与之相关的具有重要物理意义的一些数学问题至今未能解决。如,同时满足质量守恒、动量守恒和能量守恒的完全可压的Navier-Stokes方程在流入问题研究上,证明初边值两端差异大的强粘性接触间断波的渐近稳定性就是个很重要也很困难的公开问题。该问题难度主要体现在完全可压的Navier-Stokes方程如果初始温度和密度在两端状态差异很大时候方程的解是否存在,并且在初值具有一定扰动的情况下渐近极限是否达到强粘性接触间断波。本项目将从以下两方面对该问题进行探索性研究,回答上述科学问题: 1)通过抛物方程基本解理论来构造满足参考文献定义的强粘性接触间断波; 2)证明初值满足一定性质时强粘性接触间断波是渐近稳定的。
中文关键词: 流入问题;粘性接触间断波;整体解的存在性;渐近稳定性;
英文摘要: Navier-Stokes equations are one of the most important problems in hydromechanics, but many physical meanings of mathematical issues still open. For example, as to inflow problem of full compressible Navier-Stokes equations of half space, which are composed of mass conservation, momentum conservation and energy conservation equations, to work out their stability of strong viscous contact discontinuity waves still open. The main difficulty is we must face the different ends of initial temperature and density. In this project we will consider the following problems: 1) According to the definition of contact discontinuity wave we use fundmental solution of parabolic equation to construct a strong viscos contact discontinuity; 2) Proof the stabilty limits of inflow problem are just the strong viscos contact discontinuity waves.
英文关键词: inflow;viscous contact discontinutiy;global existence;asymptotic stabilty;