Navier－Stokes方程稳定性研究（Ⅱ）

Stability of Navier-Stokes Equation(Ⅱ)

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。

In this paper, the necessary conditions of the existence of C￣2 solutions in some initial problems of Navier- Stokes equatious are given,and examples of ins-tability of initial 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 equation and various authors studies this problem and contributed a nun1ber of resuIts.1.Leray,a FrenG,h professor,proved the existence of Navier一Stokes equa-tion ulder certain defind initial and boundary value conditions.In this paper,with certa in rigorously defined key concepts.based upon the basic theory of J.Hadamard partial deferential equations[1],gives a fundamental theory of insta-bility of Navier-Stokes eql1ations.Finally,many examples are given,proofs referring to reference[4].