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On the Free Surface Motion of Highly Subsonic Heat-Conducting Inviscid Flows
Archive for Rational Mechanics and Analysis ( IF 2.5 ) Pub Date : 2021-03-06 , DOI: 10.1007/s00205-021-01624-9
Tao Luo , Huihui Zeng

For the free surface problem of highly subsonic heat-conducting inviscid flow in 2-D and 3-D, a priori estimates for geometric quantities of free surfaces, such as the second fundamental form and the injectivity radius of the normal exponential map, and the Sobolev norms of fluid variables, are proved by investigating the coupling of the boundary geometry and the interior solutions. An interesting feature for the free surface problem studied in this paper is the loss of one more derivative than the problem of incompressible Euler equations, for which a geometric approach was introduced by Christodoulou and Lindblad [11]. Due to the loss of the one more derivative and loss of the symmetry of equations which create significant difficulties in closing the estimates in Sobolev spaces of finite regularity, the geometric approach in [11] needs to be substantially developed and extended by exploring the interaction of large variation of temperature, heat-conduction, non-zero divergence of the fluid velocity and the evolution of free surfaces.



中文翻译:

关于高亚音速导热无粘性流的自由表面运动

对于2-D和3-D中高亚音速导热无粘性流的自由表面问题,先验估计自由表面的几何量,例如第二基本形式和法线指数图的注入半径,以及通过研究边界几何形状与内部解的耦合来证明流体变量的Sobolev范数。本文研究的自由表面问题的一个有趣特征是,与不可压缩的欧拉方程组的问题相比,导数的损失还多,而克里斯托杜洛和林德布​​拉德为此引入了一种几何方法。 [11]。由于失去了一阶导数和方程的对称性,这在封闭有限正则性的Sobolev空间中的估计时造成了很大的困难,因此[11]中的几何方法需要通过探索相互作用的方法得到实质性的发展和扩展。温度的大变化,导热,流体速度的非零散度和自由表面的演变。

更新日期:2021-03-07
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