On The Stability Of The System Of Equations For Inviscid Adiabatic Atmospheric Motion

With the method provided by stratification theory, the properties of several important systems of quasilinear partial differential equations in hydrodynamics and atmospheric dynamics are discussed, these partial differential equations include: The Euler equation of describing inviscid compressible adiabatic fluid (call it equations setⅠ);The motion equations of adiabatic dry atmosphere with turbulent viscosity but without consideration of turbulent dissipation and aerosol (call it equations setⅡ);The anelastic equations set without consideration of turbulent viscosity (call it equations setⅢ);The anelastic equations set with consideration of turbulent viscosity (call it equations setⅣ);The discussed properties involve: topological construction ; C kstability ; the well-posedness conditions of representative initial boundary value problem;the computation of analytical solution for analytic well-posed problem, and the solvability of ill-posed problem etc.. The main conclusions are obtained as follows:1. The equations setⅠ,Ⅱ,Ⅲare C∞stable equations;and the equations setⅣis C k( k≥2)unsteady equation.2. The C∞stability of Euler equation determines C∞stability of some models when viscosity (molecule viscosity,turbulent viscosity) is neglected during atmospheric motion.3. For the equations setⅠ,Ⅱ,Ⅲ, their structures of local solution space are discussed and analyzed respectively.4. On the hypersurface {t = 0}?R4, the initial value problem established by the equations setⅠis well posed, and then the analytical solution of its analytic well-posed problem is also gained.5. For the equations setⅡ,Ⅲ, their initial value problems on the hypersurface {t = 0}?R4are ill-posed.