摘要
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.
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.
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)
