On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)

SHEN Zhen

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(5): 484-492

SHEN Zhen. On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)[J]. Applied Mathematics and Mechanics, 2003, 24(5): 484-492.

Citation:

SHEN Zhen. On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)[J]. Applied Mathematics and Mechanics, 2003, 24(5): 484-492.

Citation:

SHEN Zhen. On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)[J]. Applied Mathematics and Mechanics, 2003, 24(5): 484-492.

PDF( 348 KB)

On the Well Posedness of Initial Value Problem for Euler Equations of Incompressible Inviscid Fluid(Ⅰ)

SHEN Zhen

Department of Mathematics, Shanghai University, Shanghai 2000436, P.R.Chian

Received Date: 2001-02-08
Rev Recd Date: 2002-12-28
Publish Date: 2003-05-15

Abstract

Abstract

The ill posed initial value problem of the Euler Equations and the formal solvability of ill posed problem based on stratification theory is 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}⊆R⁴ and explain that the problem has more than one solution.
- Euler equation,
- ill posed problem,
- formal solution,
- equation secondaire

FullText(HTML)

References(8)

References

[1]	JIU Quan-sen,GU Jin-sheng.Some estimates on 2-D Euler equations[J].Advances in Mathematics,1999,28(1):55-63.
[2]	酒全森.二维Eluer方程的弱解存在性[J].汕头大学学报(自然科学报).1995,10(2):28-35.
[3]	尹全成,仇庆久.关于不可压缩的Euler方程的一类解[J].数学年刊A辑,1996,(4):495-506.
[4]	Baouendi S,Goulaouic C.Probeme de Cauchy[A].In:Seminaire Schwarz[C],Parie:Parie 11,Swarchs,1997,97-117,Expose 22.
[5]	Landau J,Lifchitz E.Mecanique des Fluides[M].Moscou:Editions Mir,1971.
[6]	SHIH Wei-hui.Solutions Analytiques de Quelques Equations aux Derives Partielles en Mecanique des Fluides[M].Paris: Hermann Paris,1992.
[7]	Ehresmann Ch.Introduction a la theorie de structures infinitesimales et des pseudo-Groupes de lie[A]In:Geometrie de Differentielle Colloques du C N r S[C].Strasdourg:Colloques du C N R S,1953,97-117.
[8]	施惟慧,陈达段,何幼桦.分层理论与非线性偏微分方程基础[M].上海:上海大学出版社,2001.