Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (5): 545-554.

• 论文 • 上一篇    下一篇

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

沈臻   

  1. Department of Mathematics, Shanghai University, Shanghai 2000436, P.R.China
  • 收稿日期:2001-02-08 修回日期:2002-12-28 出版日期:2003-05-18 发布日期:2003-05-18
  • 基金资助:
    the National Natural Science Foundation of China(19971054)

ON THE WELL POSEDNESS OF INITIAL VALUE PROBLEM FOR EULER EQUATIONS OF INCOMPRESSIBLE INVISCID FLUID(Ⅰ)

SHEN Zhen   

  1. Department of Mathematics, Shanghai University, Shanghai 2000436, P.R.China
  • Received:2001-02-08 Revised:2002-12-28 Online:2003-05-18 Published:2003-05-18
  • Supported by:
    the National Natural Science Foundation of China(19971054)

摘要: The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R4, and explain that the problem has more than one solution.

Abstract: The ill posed initial value problem of the Euler equations and the formal solvability of ill posed problem based on stratification theory are discussed. For some ill posed initial value problems, the existence conditions of formal solutions and the methods of how to construct a formal solution are given. Finally, an example is given to discuss the ill posedness of the initial value problem on hyper plane {t=0} in R4, and explain that the problem has more than one solution.

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