| 一维可压Navier-Stokes方程全局弱解的渐近性态 |
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| 引用本文： | 宋红丽. 一维可压Navier-Stokes方程全局弱解的渐近性态[J]. 纺织高校基础科学学报, 2012, 25(3): 292-298 |
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| 作者姓名： | 宋红丽 |
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| 作者单位： | 西北大学 数学系,陕西 西安,710127 |
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| 摘 要： | 研究一维情形下可压Navier-Stokes方程的自由边值问题.假设初始密度间断连续到真空.先通过建立一些先验估计式得到密度ρ的正上下界,再利用磨光初值法构造光滑逼近解.当粘性系数μ（ρ）=1＋θρθ,θ〉0时,证明了弱解的全局存在性,进而讨论了全局弱解的渐近性态.
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| 关 键 词： | Navier-Stokes方程 自由边值 存在性 渐近性态 |
Asymptotic behavior of global weak solutions to 1D compressible Navier-Stokes equations |
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| SONG Hong-li. Asymptotic behavior of global weak solutions to 1D compressible Navier-Stokes equations[J]. Basic Sciences Journal of Textile Universities, 2012, 25(3): 292-298 |
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| Authors: | SONG Hong-li |
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| Affiliation: | SONG Hong-li(Department of Mathematics,Northwest University,Xi′an 710127,China) |
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| Abstract: | One-dimensional compressible Navier-Stokes equations with free boundary value problem is studied.The initial density is assumed to be connected to vacuum discontinuously.The positive upper and lower bound of the density ρ is obtained by using some priori estimates,and then smooth approximate solutions are constructed by defining the approximate initial data.The existence of global weak solutions is proved when the viscosity coefficient μ(ρ)=1+θρθ,θ>0.Moreover,asymptotic behavior of global weak solutions is discussed. |
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| Keywords: | Navier-Stokes equation free boundary existence asymptotic behavior |
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