等熵Chaplygin气体的平面波解

数学物理学报 ›› 2016, Vol. 36 ›› Issue (4): 681-689.

等熵Chaplygin气体的平面波解

黄守军, 王蕊

安徽师范大学数学与计算机科学学院安徽芜湖 241000

收稿日期:2015-10-11 修回日期:2016-04-16 出版日期:2016-08-26 发布日期:2016-08-26
作者简介:黄守军,sjhuang@mail.ahnu.edu.cn;王蕊,wangrui8987@126.com
基金资助:
国家自然科学基金（11301006）和安徽省自然科学基金（1408085MA01）资助

Plane Wave Solutions to the Euler Equations for Chaplygin Gases

Huang Shoujun, Wang Rui

School of Mathematics and Computer Science, Anhui Normal University, Anhui Wuhu 241000

Received:2015-10-11 Revised:2016-04-16 Online:2016-08-26 Published:2016-08-26
Supported by:
Supported by the NSFC(11301006)and the Natural Science Foundation of Anhui Province(1408085MA01)

摘要/Abstract

摘要：

研究等熵 Chaplygin气体的平面波解，给出平面波解的若干有趣性质，并特别指出平面波解所满足的微分方程组可以逐步求解，从而得到等熵Chaplygin气体光滑平面波解的整体存在性. 此外，给出平面波解的若干爆破结果.

关键词: Euler方程组, Chaplygin 气体, 平面波解, 整体存在, 爆破

Abstract:

In this paper, we consider the plane wave solutions to the Euler equations for isentropic Chaplygin gases. Some interesting properties enjoyed by plane wave solutions are explored. In particular, the reduced system for the plane wave solutions of Chaplygin gases can be solved successively. Based on this, we are able to obtain the global existence of smooth plane wave solutions for isentropic Chaplygin gases. Some results on the blow up phenomena are also discussed.

Key words: Euler equations, Chaplygin gases, Plane wave solution, Global existence, Blow up phenomena

中图分类号:

O175.2

黄守军, 王蕊. 等熵Chaplygin气体的平面波解[J]. 数学物理学报, 2016, 36(4): 681-689.

Huang Shoujun, Wang Rui. Plane Wave Solutions to the Euler Equations for Chaplygin Gases[J]. Acta mathematica scientia,Series A, 2016, 36(4): 681-689.

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