Sonic-subsonic limit of approximate solutions to multidimensional steady Euler equations
主 题: Sonic-subsonic limit of approximate solutions to multidimensional steady Euler equations
报告人: Professor Feimin Huang (Academy of Mathematics and System Sciences, Academia Sinica)
时 间: 2013-11-08 14:00-15:00
地 点: 理科一号楼1114（数学所活动）
A compactness framework is established for approximate solutions to sonic-subsonic flows governed by the steady full Euler equations for compressible fluids in arbitrary dimension. The existing compactness frameworks for the two-dimensional potential case do not directly apply for the steady full Euler equations in higher dimensions. In particular, the framework applies for both non-isentropic and rotational flows. One of our main observations is that the compactness can be achieved by using only natural weak estimates for the mass balance and the vorticity, along with the Bernoulli law and the entropy relation, through a more delicate analysis on the phase space. We then establish the compactness framework for approximate solutions to sonic-subsonic flows in any dimension. As direct applications, we establish several existence theorems for multidimensional sonic-subsonic for Euler flows through infinitely long nozzles. This talk is based on joint works with G.Q.Chen, T.Y.Wang and Y. Wang.