| 可压缩Navier-Stokes方程行波解的渐近稳定性 |
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| 引用本文： | 周培培,陈亚洲,李艳军,施小丁. 可压缩Navier-Stokes方程行波解的渐近稳定性[J]. 北京化工大学学报(自然科学版), 2008, 35(5): 107-111 |
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| 作者姓名： | 周培培 陈亚洲 李艳军 施小丁 |
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| 作者单位： | 北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029;北京化工大学理学院,北京,100029 |
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| 摘 要： | 研究了一维黏性可压缩Navier-Stokes方程组,给出了在小扰动条件下冲击波解的渐近稳定性。考虑在小的初始扰动下黏性冲击波解的叠加，通过局部解的存在唯一性分析和先验估计，得到此时的黏性冲击波解是渐近稳定的。证明通过能量估计方法给出。
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| 关 键 词： | 可压缩Navier-Stokes方程 冲击波 渐近稳定性 能量估计 |
| 收稿时间： | 2008-03-24 |
Asymptotic stability of solutions for one-dimensional compressible Navier-Stokes equations |
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| ZHOU PeiPei,CHEN YaZhou,LI YanJun,SHI XiaoDing. Asymptotic stability of solutions for one-dimensional compressible Navier-Stokes equations[J]. Journal of Beijing University of Chemical Technology, 2008, 35(5): 107-111 |
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| Authors: | ZHOU PeiPei CHEN YaZhou LI YanJun SHI XiaoDing |
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| Affiliation: | School of Science,Beijing University of Chemical Technology, Beijing 100029, China |
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| Abstract: | One-dimensional compressible Navier-Stokes equations have been investigated,and the asymptotic stability of the shock wave has been established under conditions of small perturbation.A superposition of the shock wave has been derived under conditions where the initial disturbance is sufficiently small.By the means of existence and uniqueness of the local solution and the priori estimates,the superposition of the shock wave is shown to have asymptotic stability.The proof is based on the elementary energy method. |
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| Keywords: | compressible Navier-Stokes equations shock wave asymptotic stability energy method |
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