Navier-Stokes方程稳定性研究(Ⅲ)

施惟慧

Navier-Stokes方程稳定性研究(Ⅲ)

施惟慧

上海大学

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出版历程
- 收稿日期: 1994-01-20
- 刊出日期: 1994-12-15

A Stability Study of Navier-Stokes Equations(Ⅲ)

Shi Wei-hui

Shanghai University, Shanghai

摘要

摘要: 本文给出Navier-Stokes方程某些初值问题存在C²解的必要条件,并给出其在{t=0}上的初值问题不适定的例证。Navier-Stokes方程的初值问题是研究这个方程的基础问题之一。国内外很多学者在这方面的研究曾取得了不同程度的结果。法国时J.Leray教授就曾在某种意义下证明过Navier-Stokes方程某种初边值问题解的存在性^[3].本文根据J.Hadamard的偏微分方程的基础理论^[1].给出某些关键问题的严格定义,叙述一个有关Navipr-Stokes方程不稳定的基本定理。最后给出若干例证,其证明可参见^[4].
- Ehresmann空间 /
- 本方程 /
- Cauchy问题
Abstract: In this paper, the necessary conditions of the existence of C² solution. in someinitial problems of Navier-Stokes equations are given. and examples of instability ofinitial value (at t=0) problems are also given. The initial value problem of Navier-Stokes equation is one of the most fundamental problem for this equationvarious authors studies this problem and contributed a number of results.J.Leray.a French professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions.In this paper,with certain rigorously defined key concepts,based upon the basic theory of J.Hadmard partial differential equanous[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to reference.[4].
- Ehresmann space /
- basic equation /
- Cauchy problem

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参考文献(5)

[1]	Hadamard, J.,Le Probleme de Cauchy et les Epeaiion aux Derives Partielles Lineaires Hyperboliques, Harmann, Paris(1939), Lo Theorie des Equations aux Derivees Partielles, Editions Scientifiques, Pekin(1964).
[2]	Landau, L, and E, Lifcuiez, Physique Thceorique, Tome 6, Edition Mir Moscou(1971).
[3]	Leray,J.Essai sur le mouvement plan d'un liquide visqucuz que limitent des parois, Journal Mathematique(1934).
[4]	Shih,W.H.Solutions Anaiytiques de Quelques Equations aux Derivees Portiellss en Mecanique des Fluides, Hermann, Paris(1992).
[5]	Shih, W, S,,Une methode elemcntaire pour I'etude des equatioas aux derivees partielles, Diagrammes 16, Paris(1986), C, R.Acad, Sc, Paris, 303, Serie I.(1986), 439-441, 304 Serie I (1987), 103-106, 187-190, 535-538.