中山大学学报自然科学版 ›› 2018, Vol. 57 ›› Issue (6): 131-134.doi: 10.13471/j.cnki.acta.snus.2018.06.017

• 论文 • 上一篇    下一篇

带阻尼的非等熵欧拉方程组的爆破

董建伟,杨永   

  1. 郑州航空工业管理学院理学院,河南 郑州 450015
  • 收稿日期:2017-12-06 出版日期:2018-11-25 发布日期:2018-11-25

Blowup for the non-isentropic Euler equations with damping

DONG Jianwei, YANG Yong   

  1. School of Mathematics and Physics, Zhengzhou University of Aeronautics,Zhengzhou 450015, China
  • Received:2017-12-06 Online:2018-11-25 Published:2018-11-25

摘要:

研究带阻尼的非等熵欧拉方程组初边值问题解的爆破现象。利用积分方法证明了当与初始动量有关的加权泛函充分大时,其解将在有限时刻爆破。将近来已知的爆破结果由等熵情形推广到非等熵情形,并在没有绝热常数不大于3的限制下得到了负初始熵情形的爆破结果。

关键词: 带阻尼的非等熵欧拉方程组, 初边值问题, 爆破

Abstract:

The blowup phenomena of the solutions for the initial-boundary value problem of the non-isentropic Euler equations with damping is studied. It is proved that the solutions will blow up in finite time when a weighed functional associated with the initial momentum is large enough by using the integration method. Some recently known blow-up results are extended from the isentropic case to the non-isentropic case. And the blow-up result for the negative initial entropy case is obtained without the restriction that the adiabatic constant is not bigger than three.

Key words: non-isentropic Euler equations with damping, initial-boundary value problem, blowup

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