一维可压Navier-Stokes方程自由边值问题的自模解  

Self-similar solutions to 1D compressible Navier-Stokes equations with free boundary problem

作　　者：宋红丽[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2013年第1期36-42,共7页Basic Sciences Journal of Textile Universities

摘　　要：研究黏性系数μ(ρ)=1+θρθ时一维可压Navier-Stokes方程自模解的非存在性.首先通过建立能量估计式,熵估计式得到密度函数ρ的正的下界,然后对能量函数进行定量分析,利用能量爆破理论证明了θ>0时一维可压Navier-Stokes方程不存在具有有限总能量的自模解.最后将常黏性系数Navier-Stokes方程自模解的方法推广到黏性系数依赖于密度的情形,并且把θ的范围扩展到θ>0.The non-existence of self-similar solutions to one-dimensional compressible Navier-Stokes equations is studied when the viscosity coefficient/.t（p） =1＋θρ^θ. The positive lower bound of the density p is obtained by establishing energy estimate and entropy estimate. By quantitative analysis to energy function and using energy blowing-up theory, there exist neither forward nor backward self-similar solutions with finite total energy when θ〉 0. This generalizes the method of studying the compressible Navier-Stokes equations with constant viscosity coefficient to the density-dependent viscosity coefficient and enlarging the interval of θ to θ〉0.

关 键 词：NAVIER-STOKES方程 自由边值 自模解 非存在性 

分 类 号：O175.2[理学—数学]