One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, （i） the inertial force has no influence on the criterion of the well-posed Cauchy problem; （ii） th...One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, （i） the inertial force has no influence on the criterion of the well-posed Cauchy problem; （ii） the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; （iii） this type of atmosphere evolution equations is ill-posed on the hyperplane t = 0 in spite of its compressibility and viscosity; （iv） the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.展开更多
The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some repr...The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local （exact） solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.展开更多
The system of equation discussed in this paper is a model that describes the phenomena of El Nino and Southern Oscillation （ENSO）. The stability of this model is studied with the method of stratification theory. A n...The system of equation discussed in this paper is a model that describes the phenomena of El Nino and Southern Oscillation （ENSO）. The stability of this model is studied with the method of stratification theory. A necessary and sufficient condition to justify whether an initial （boundary） problem is well posed or not is also obtained.展开更多
It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal ...It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal solution of some representative ill-posedness initial-boundary value problem are presented. Finally, an example is also given.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos.40233027 and 90411006)the National Natural Science Foundation of China (Major Program) (No.90411006)
文摘One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, （i） the inertial force has no influence on the criterion of the well-posed Cauchy problem; （ii） the compressibility plays no role on the well-posed condition of the Cauchy problem of the viscid atmosphere equations, but changes the well-posed condition of the viscid atmosphere equations; （iii） this type of atmosphere evolution equations is ill-posed on the hyperplane t = 0 in spite of its compressibility and viscosity; （iv） the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.
文摘The well-posedness of the initial value problem of the Euler equations was mainly discussed based on the stratification theory, and the necessary and sufficient conditions of well-posedness are presented for some representative initial or boundary value problem, thus the structure of solution space for local （exact） solution of the Euler equations is determined. Moreover the computation formulas of the analytical solution of the well-posed problem are also given.
基金supported by the National Natural Science Foundation of China (Grant No.90411006)
文摘The system of equation discussed in this paper is a model that describes the phenomena of El Nino and Southern Oscillation （ENSO）. The stability of this model is studied with the method of stratification theory. A necessary and sufficient condition to justify whether an initial （boundary） problem is well posed or not is also obtained.
基金Project supported by the National Natural Science Foundation of China （Major Program of the Tenth Five-Year Plan） （Grant No,90411006）
文摘It is proved that the ill-posed initial value problem of the Euler equations for compressible adiabatic inviscid fluid flow can be only formally solved. The necessary and sufficient conditions for existence of formal solution of some representative ill-posedness initial-boundary value problem are presented. Finally, an example is also given.
