高亚音速导热无粘流的自由表面运动
On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid Flows
摘要：
对于一个高亚音速导热无粘流的自由面问题，在Christodoulou和Lindblad研究不可压无粘流自由面问题的几何方法的启发下，通过确定一个合适的高阶能量泛函，在Taylor符号条件下证明了二维和三维Sobolev范数的先验估计.给出了自由表面法向指数映射的第二基本型和内射半径等几何量的估计。在我们的分析中的新颖性包括处理强耦合的大的变化的温度，热传导，流体的可压缩性和自由表面的演变，损失的对称性方程，并在关闭的参数，这是一个关键功能相比，Christodoulou和Lindblad的工作的导数损失。本文的动机是有助于理解热传导对无粘可压缩流的自由表面运动所起的作用以及当马赫数较小时这种运动的行为。
英文摘要：
For a free surface problem of a highly subsonic heat-conducting inviscid flow, motivated by a geometric approach developed by Christodoulou and Lindblad in the study of the free surface problem of incompressible inviscid flows, the a priori estimates of Sobolev norms in 2-D and 3-D are proved under the Taylor sign condition by identifying a suitable higher order energy functional. The estimates for some geometric quantities such as the second fundamental form and the injectivity radius of the normal exponential map of the free surface are also given. The novelty in our analysis includes dealing with the strong coupling of large variation of temperature, heat-conduction, compressibility of fluids and the evolution of free surface, loss of symmetries of equations, and loss of derivatives in closing the argument which is a key feature compared with Christodoulou and Lindblad's work. The motivation of this paper is to contribute to the program of understanding the role played by the heat-conductivity to free surface motions of inviscid compressible flows and the behavior of such motions when the Mach number is small.
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