Cauchy problem of one type of atmosphere evolution equations. (English) Zbl 1165.76057
Summary: We discuss a class of atmosphere evolution equations. It is found that, according to the stratification theory, (i) the inertial force has no influence on the well-posedness of the Cauchy problem; (ii) the compressibility plays no role in the well-posedness condition for the Cauchy problem for viscous atmosphere equations, but changes the well-posedness condition for the considered 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 for compressible viscous atmosphere with no initial motion is ill-posed.
MSC:
| 76U05 | General theory of rotating fluids |
| 35Q35 | PDEs in connection with fluid mechanics |
| 86A10 | Meteorology and atmospheric physics |
References:
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