| 刘见礼,朱磊.一维可压缩Euler方程组的两个模型*[J].数学年刊A辑,2015,36(4):345~354 |
| 一维可压缩Euler方程组的两个模型* |
| Two Models of 1-D Compressible Euler Equations |
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| DOI： |
| 中文关键词: 可压缩Euler方程组, 经典解, Cauchy~问题 |
| 英文关键词:Compressible Euler equations, Classical solutions, Cauchy problem |
| 基金项目:本文受到国家自然科学基金(No.11401367)和教育部博士点基金(No.20133108120002)的资助. |
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| 中文摘要: |
| 作者考察了一维可压缩~Euler~方程组的两个模型.
利用特征分解和~Gronwall~不等式, 首先得到具有几何结构
且绝热指数 $\gamma
=3$ 的一维可压缩~Euler~方程组 $L^\infty$ 模的一致有界性. 进一步,
考虑当绝热指数 $\gamma = -1$ 时,
一维非等熵可压缩~Euler~方程组的~Cauchy~问题. 在适当的假设下,
得到该系统的整体经典解. |
| 英文摘要: |
| This paper deals with two models of 1-D compressible Euler equations. Firstly,
the authors give 1-D compressible Euler equations with geometrical structure and adiabatic
index
= 3, and get a uniform L∞ bound of solutions. Secondly, the authors consider the
Cauchy problem for the 1-D Chaplygin gas in nonisentropic case, when the adiabatic index
is
= ?1. Under appropriate assumptions on initial data, the global existence of classical
solutions with uniform bound is obtained. |
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