On the global existence and uniqueness of solutions to the nonstationary boundary layer system  

作　　者：ZHANG Jianwen ZHAO Junning 

机构地区：[1]School of Mathematical Sciences, Xiamen University, Xiamen 361005, China School of Mathematical Sciences, Xiamen University, Xiamen 361005, China

出　　处：《Science China Mathematics》2006年第7期932-960,共29页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China (Grant No. 10131050).

摘　　要：In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.In this paper, we study the problem of boundary layer for nonstationary flows of viscous incompressible fluids. There are some open problems in the field of boundary layer. The method used here is mainly based on a transformation which reduces the boundary layer system to an initial-boundary value problem for a single quasilinear parabolic equation. We prove the existence of weak solutions to the modified nonstationary boundary layer system. Moreover, the stability and uniqueness of weak solutions are discussed.

关 键 词：boundary layer  BV space  GLOBAL WEAK solutions  stability and uniqueness. 

分 类 号：N[自然科学总论]