Abstract
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.
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Communicated by LI Ji-bin
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)
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He, Jx., He, Yh. Cauchy problem of one type of atmosphere evolution equations. Appl Math Mech 27, 1409–1416 (2006). https://doi.org/10.1007/s10483-006-1013-y
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DOI: https://doi.org/10.1007/s10483-006-1013-y