Symmetric nonbarotropic flows with large data and forces

被引:60
作者
Hoff, D [1 ]
Jenssen, HK
机构
[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA
[2] N Carolina State Univ, Dept Math, Raleigh, NC 27695 USA
关键词
D O I
10.1007/s00205-004-0318-5
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We prove the global existence of weak solutions of the Navier-Stokes equations of compressible, nonbarotropic flow in three space dimensions with initial data and external forces which are large, discontinuous, and spherically or cylindrically symmetric. The analysis allows for the possibility that a vacuum state emerges at the origin or axis of symmetry, and the equations hold in the sense of distributions in the set where the density is positive. In addition, the mass and momentum equations hold weakly in the entire space-time domain, but with a nonstandard interpretation of the viscosity terms as distributions. Solutions are obtained as limits of solutions in annular regions between two balls or cylinders, and the analysis allows for the possibility that energy is absorbed into the origin or axis, and is lost in the limit as the inner radius goes to zero.
引用
收藏
页码:297 / 343
页数:47
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