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A NOTE ON THE EXISTENCE AND NONEXISTENCE OF GLOBALLY BOUNDED CLASSICAL SOLUTIONS FOR NONISENTROPIC GAS DYNAMICS

林龙威; 黄锡荣   

  1. 澳门大学理学院
  • 收稿日期:2004-11-15 修回日期:1900-01-01 出版日期:2006-07-20 发布日期:2006-07-20
  • 通讯作者: 黄锡荣

A NOTE ON THE EXISTENCE AND NONEXISTENCE OF GLOBALLY BOUNDED CLASSICAL SOLUTIONS FOR NONISENTROPIC GAS DYNAMICS

Lin Longwei; Vong Seakweng   

  1. Faculty of Science and Technology, University of Macau, Macau, China
  • Received:2004-11-15 Revised:1900-01-01 Online:2006-07-20 Published:2006-07-20
  • Contact: Vong Seakweng

摘要:

Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.

关键词: Nonisentropic gas dynamics system, global smooth resolvability, Cauchy problem

Abstract:

Existence of globally bounded classical solution for nonisentropic gas dynamics system has long been studied, especially in the case of polytropic gas. In [4], Liu claimed that sufficient condition has been established. However, the authors find that the argument he used is not true in general. In this article, the authors give a counter example of his argument. Hence, his claim is not valid. The authors believe that it is difficult to impose general conditions on the initial data to obtain globally bounded classical solution.

Key words: Nonisentropic gas dynamics system, global smooth resolvability, Cauchy problem

中图分类号: 

  • 35L65