Navier-Stokes方程稳定性研究(Ⅱ)
Stability of Navier-Stokes Equation(Ⅱ)
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摘要: 本文对Navier-Stokes方程与热传导方程的性质进行了比较。法国数学家、偏微分方程权威J.Leray教授在其对Navier-Stokes方程的研究中,曾由热传导方程出发而求得Navier-Stokes方程某种初(边)值问题的适定性结果[2].巴黎十一大学的R.Temam等专家、教授也曾多次提出过将两类方程类比的疑问。本文试将其中根本不同点做了叙述和例证。
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关键词:
- Navier-Stokes方程 /
- 解空间 /
- Janet数
Abstract: In this paper.we make some comparisons between the solutions for Narier-Stokes equation and those.for heat conduction equation.In his study of Navier-Stokes equation.Professor J.Leray.a French mathematician and authority on partial differential equation,starting from heat conduction equation,obtained some results of properly posed of certain initial boundary value problems of Navier-Stokes equation.Professor R.Temam of University de Paris XI and other experts in this field also brought up the possibility of comparing these two classes of equations.This paper attempts to describe and provethe.fundamental difference between these two.-
Key words:
- solution space /
- Janet number /
- Nayler-Stokes equation
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[1] Laudau,L.and E.Lifchitz,Mecanique des Fluid,Edition Tome 6,Mir Mouscou(1971). [2] Leray,J,Essai sur les mouvements plans d'un liquide visqueux que limitent des parois Journal Mathematique(1934). [3] Mikhailov,V.Equations aux Derive.ss Partielles,Edition Mir Mouseou(1980),345-346. [4] Shih,W.S.,Un invariant numerique associe a unsysteme d'equations aux derivees partielles,C.R.Acad Sc Paris,Serie 1,304,17(1987). [5] Shih,W.H.Solutions analytiques de quelques equations aux derivees partielles en mecanique des fluides,travaux en cours,42,Hermann,Paris(1992). [6] Valiron G.,Equations Fonctionnelles,Applications,Hermann(1992),587-589. -
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