关键词: two-phase flow, numerical simulation, TVD schemes, detonation wave

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 ofNavier-Stokes equation is one of the most fundamental problem for this equationvarious authors studies this problem and contributed a number of results.J.Leray.aFrench professor, proved the existence of Navier-Stokes equation under certain definedinitial and boundary value conditions.In this paper,with certain rigorously definedkey.concepts,based upon the basic theory of J.Hadmard partial differentialequanous[1], gives a fundamental theory of instability of Navier-Stokes equations.Finally,many examples are given,proofs referring to Ref.[4].

Key words: two-phase flow, numerical simulation, TVD schemes, detonation wave