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Some conclusions about the smooth function classes stability for the basic system of equations of atmospheric motion and instability for Navier-Stokes equation are summarized. On the basis of this, by taking the basic system of equations of atmospheric motion via Boussinesq approximation as example to explain in detail that the instability about some simplified models of the basic system of equations for atmospheric motion is caused by the instability of Navier-Stokes equation, thereby, a principle to guarantee the stability of simplified equation is drawn in simplifying the basic system of equations. 相似文献
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施惟慧 《应用数学和力学(英文版)》1994,(12)
ASTABILITYSTUDYOFNAVIER-STOKESEQUATIONS(Ⅲ)ShiWei-hui(施惟慧)(shanghaiUniversily.Shanghai)(ReceivedJan.20.1994;CommunicatedbyChie... 相似文献
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Applying the theory of stratification, it is proved that the system of the two-dimensional non-hydrostatic revolving fluids is unstable in the two-order continuous function class. The construction of solution space is given and the solution approach is offered. The sufficient and necessary conditions of the existence of formal solutions are expressed for some typical initial and boundary value problems and the calculating formulae to formal solutions are presented in detail. 相似文献
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I.IntroductionItiswidelyknownthattheexactsolutiontocertainpartialdifferentialequationsplaysanimportantroleintheresearchofphysicsandmechanicsproblems.AndforsQmeequations,tthoseexarts0lutioncannotbeobtained,theFrenchmathematicianE.Picardonceintroducedfinite… 相似文献
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STABILITYOFNAVIER-STOKESEQUATION(II)ShiWei-hui(施惟慧);FangXiao-zuo(方晓佐)(ShanghaiUniversity),Shanghai(ReceivedDec.11,1993;Commun... 相似文献
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ONTHESTABILITYOFFORCEDDISSIPATIVENONLINEARSYSTEM¥ChenDaduan(陈达段)LiuXiaoming(刘晓明)ShiWeihui(施惟慧)(ShanghaiUniversity.Shanghai200... 相似文献
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Inreference [1 ] ,wediscussedtheinstabilityofNavier_StokesequationonR3×R ,and ,intheillustrationofit,wepresentedsomeexamplesintheformofexactsolution .Thebasisoftheconstructionofthemisthe“equationsecondaire”oftheequation .Infact,theseexactsolutionsaresomelimit… 相似文献
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Stability related to theoretical model for catastrophic weather prediction, which includes non-hydrostatic perfect elastic model and anelastic model, is discussed and analyzed in detail. It is proved that non-hydrostatic perfect elastic equations set is stable in the class of infinitely differentiable function. However, for the anelastic equations set, its continuity equation is changed in form because of the particular hypothesis for fluid, so "the matching consisting of both viscosity coefficient and incompressible assumption" appears, thereby the most important equations set of this class in practical prediction shows the same instability in topological property as Navier-Stokes equation, which should be avoided first in practical numerical prediction. In light of this, the referenced suggestions to amend the applied model are finally presented. 相似文献
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