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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[1] Oliger J,Sundstrom A.Theoretical and practical aspects of some initial-boundary value problems in the field dynamics[J].SIAM J Appl Math,1978,35(3):419—446. doi: 10.1137/0135035 [2] 曾庆存.数值天气预报的数学物理基础[M].北京:科学出版社,1979. [3] 穆穆.广义涡度方程初边值问题的整体光滑解及其应用[J].中国科学,A辑,1986,29(11):1153—1163. [4] Temam Roger, WANG Shou-hong.Mathematical problems in meteorology and oceanography[J].Bull Amer Meteorol Soc,2000,81(2):319—321. doi: 10.1175/1520-0477(2000)081<0319:MPIMAO>2.3.CO;2 [5] 施惟慧,陈达段,何幼桦.分层理论与非线性偏微分方程基础[M].上海:上海大学出版社,2001. [6] 陈达段,刘晓明,施惟慧.关于强迫耗散非线性系统的稳定性[J].应用数学和力学,1996,17(6):515—522. [7] 何幼桦,施惟慧.带未知函数多项式附加项的Navier-Stokes方程的Ck不稳定性[J].应用数学和力学,2000,21(12):1301—1309.
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