On the Cauchy Problem of One Type of Atmosphere Evolution Equations
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摘要: 在分层理论的框架下讨论一类大气演化方程组的Cauchy问题,证明了:1) 惯性力对一类大气演化方程组Cauchy问题的适定性判别标准没有影响;2) 可压缩性对粘性大气方程组Cauchy问题的适定性判别标准没有影响，但对无粘大气方程组，可压缩性改变Cauchy问题适定性判别标准;3) 所论方程组在t=0超平面上的Cauchy问题均是不适定的,并不受粘性和可压缩性的影响;4) 可压无粘大气方程与运动静止初始条件构成的Cauchy问题是不适定的．Abstract: One type of evolution atmosphere equations was discussed. It is found that according to the stratification theory, 1) the inertial force has no influence on the criterion of the well-posed Cauchy problem; 2) 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; 3) this type of atmosphere evolution equations is ill-posed on the hyperplane t=0 in spite of its compressibility and viscosity; 4) the Cauchy problem of compressible viscosity atmosphere with still initial motion is ill-posed.
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Key words:
- well-posedness /
- viscosity /
- compressibility /
- stratification theory
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