项目名称: 可压缩Navier-Stokes方程全局光滑解的适定性问题
项目编号: No.11201310
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 段琴
作者单位: 深圳大学
项目金额: 22万元
中文摘要: 可压缩Navier-Stokes方程及相关模型的解的适定性问题是应用数学及流体动力学中的一个重要课题。一直以来,也是国内外关心的主要问题。本项目旨在研究高维可压Navier-Stokes方程全局光滑解的适定性。 由于方程是一个双曲- - 抛物耦合的非线性方程,并且密度允许真空,这为我们的研究带来了很大的困难。 本项目主要围绕两个方面展开。一是研究有界区域上带有Navier边界条件或者Dirichlet边界条件的可压Navier-Stokes方程全局光滑解的适定性。另一方面即是对外区域问题以及可压Full Navier-Stokes方程的解的适定性研究。我们拟借助等熵流适定性方面的研究方法及最新进展, 把相关结论推广到高维可压缩Full Navier-Stokes方程中。
中文关键词: 可压缩;Navier-Stokes方程;适定性;;
英文摘要: The global well-posedness of classical solutions for the compressible Navier-Stokes system and related models is a very important problem to the applied mathematics and fluid dynamics. In this project, we want to study the global well-posedness of classical solutions for the high-dimensional compressible Navier-Stokes equations. Since the system is a nonlinear hyperbolic - parabolic system and the density allows vacuum, so it is very difficult to study the problem. We mainly discuss the following two aspects: 1. Investigate the global well-posedness of classical solutions to the bounded domain with Naiver boundary condition or Dirichlet boundary condition. 2. Study the global well-posedness of solutions to the exterior domain and the full Navier-Stokes system. We hope to extend well-posedness of solutions to the high-dimensional compressible full Navier-Stokes equations by use of the method and recent developments in the isentropic fluid.
英文关键词: compressible;Navier-Stokes equation;well-posedness;;