MIXED EQUATIONS AND TRANSONIC FLOW
MIXED EQUATIONS AND TRANSONIC FLOW
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DOI：
10.1142/s0219891604000081
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发表时间：
2004-03
影响因子：
0.7
通讯作者：
C. Morawetz
中科院分区：
文献类型：
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作者：
C. Morawetz
本文综述了混合方程存在唯一性定理的研究现状及其在跨声速流动问题中的应用。对一些新问题进行了介绍和讨论。在非常简短地讨论了依赖于时间的流动(Sec.1)在SEC中描述了稳态及其历史。2.单位：秒。3和4，描述了混合方程的早期工作及其与二维流的联系。5提出了激波问题、良好翼型的构造及相应的边值问题。在证券交易委员会。我们来看看两个线性摄动问题可以告诉我们什么关于流动的信息。在证券交易委员会。7我们描述了引起类似问题的流体问题的其他例子。第8节专门讨论守恒定律和SECS的独特性。9-11给出了弗里德里希乘子的存在性证明。在证券交易委员会。12给出了与前面的一些例子相对应的定常流动的存在的证明，但方程已被修改为具有小参数的高阶系统，当设为零时，得到了跨音速流动的方程。这还有待于证明，这一正式的限制确实成立。许多都被遗漏了，特别是现代的计算结果，文本反映了作者的特殊兴趣。
This paper reviews the present situation with existence and uniqueness theorems for mixed equations and their application to the problems of transonic flow. Some new problems are introduced and discussed. After a very brief discussion of time-dependent flows (Sec. 1) the steady state and its history is described in Sec. 2. In Secs. 3 and 4, early work on mixed equations and their connection to 2D flow are described and Sec. 5 brings up the problem of shocks, the construction of good airfoils and the relevant boundary value problems. In Sec. 6 we look at what two linear perturbation problems could tell us about the flow. In Sec. 7 we describe other examples of fluid problems giving rise to similar problems. Section 8 is devoted to the uniqueness by a conservation law and Secs. 9–11 to the existence proofs by Friedrichs' multipliers. In Sec. 12 a proof is given of the existence of a steady flow corresponding to some of the previous examples but the equations have been modified to a higher order system with a small parameter which when set to zero yields the equations of transonic flow. It remains to show that this formal limit really holds. Much has been left out especially modern computational results and the text reflects the particular interests of the author.