两个大气动力学模式整体强解的存在唯一性
Existence and Uniqueness of Global Strong Solutions of Two Models in Atmospheric Dynamics
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摘要: 文中用能量估计的方法,证明了大气动力学中的基本模式——正压无辐散模式与斜压准地转-准无辐散模式整体强解的存在唯一性,从而推广了作者在文[3]～[5]中所得到的结果并证实了曾庆存在[1]中的一个猜测.Abstract: In this paper, the author proves by the methods of energy estimates the existence and uniqueness of global strong solutions of barotropic nondivergent model and baroclinic quasi-geostrophic quasi-nondivergent model.The two models are fundamental ones in atmospheric dynamics. The results here generalize the outcome given by the author in [3]-[5] and verify a conjecture posed by Zeng Qing-cun in [1].
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[1] 曾庆存,《数值天气预报的数学物理基础》,第一卷,科学出版社,北京(1979). [2] Holton,J,R.,An Introduction to Dynamic Meteorology,Academic Press,Inc,(1972). [3] 穆穆,非线性涡度方程初边值问题的整体光滑解及其应用,数学物理学报(待发表). [4] 穆穆,非线性涡度方程Cauchy问题的整体光滑解及其应用,投数学年刊. [5] 穆穆,非线性涡度方程的若干定解问题,复旦大学博士学位论文(1985). [6] Adams,R,A.,Sobolev Spaces,New York,Academic Press(1975). [7] Triebel,H.,Interpolation Theory,Function Space,Differential Operators,North-Hol-land Publishing Company(1978). -
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