Applied Mathematics and Mechanics

, Volume 24, Issue 5, pp 555–567 | Cite as

On the well posedness of initial value problem for euler equations of incompressible inviscid fluid (II)

  • Shen Zhen
Article
  • 19 Downloads

Abstract

The solvability of the Euler equations about incompressible inviscid fluid based on the stratification theory is discussed. And the conditions for the existence of formal solutions and the methods are presented for calculating all kinds of ill-posed initial value problems. Two examples are given as the evidences that the initial problems at the hyper surface does not exist any unique solution.

Key words

Euler equation ill-posed problem formal solution equation secondaire 

Chinese Library Classification

O175.29 

2000 MR Subject Classification

35Q05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    SHIH Wei-hui.Solutions Analytiques de Quelques Equations aux Derives Partielles en Mecanique des Fluides[M]. Paris: Hermann, 1992.Google Scholar
  2. [2]
    JIU Quan-sen, GU Jin-sheng. Some estimates on 2-D Euler equations[J].Advances in Mathematics, 1999,28(1):55–63.Google Scholar
  3. [3]
    JIU Quan-sen. The 2-dimension Eluer equations feasible existence[J].Shantou University Transaction (Science), 1995,10(2):28–35. (in Chinese)Google Scholar
  4. [4]
    YIN Hui-cheng, CHOU Qing-jiu. One type solution about the compressible Eluer equations[J].Mathematical Annual A, 1996, (4):495–506. (in Chinese)Google Scholar
  5. [5]
    SHEN Zhen. On the well postedness of initial value problem for Euler equations of incompressible inviscid fluid (I)[J].Applied Mathematics and Mechanics (English Edition), 2003,24(5):545–554.MathSciNetGoogle Scholar
  6. [6]
    Landau J, Lifchitz E.Mecanique des Fluides[M]. Moscow: Editions Mir, 1971.Google Scholar
  7. [7]
    SHIH Wei-hui, CHEN Da-duan, HE You-hua.Equation Secondaire and Nonlinear P D E Basis [M]. Shanghai: Shanghai University Press, 2001. (in Chinese)Google Scholar
  8. [8]
    Baouendi S, Goulaouic C. Probeme de Cauchy[A]. In:Seminaire Schwarz[C]. Parie: Parie 11, Expose 22, 1997, 97–117.Google Scholar
  9. [9]
    Ehresmann Ch. Introduction a la theorie de structures infinitesimales et des pseudo-groupes de lie [A]. In:Geometrie Diffierentielle de Collques du C N R S[C]. Strasdourg: Colloques du C N R S, 1953,97–117.Google Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2003

Authors and Affiliations

  • Shen Zhen
    • 1
  1. 1.Department of MathematicsShanghai UniversityShanghaiP. R. China

Personalised recommendations