AI 中文总结
本文针对气体动力学欧拉系统，确定了一类初始数据，其产生的弱解为仅取有限常数状态的离散解，且随时间趋于无穷时达到规定终端熵剖面。
AI 中文摘要
凸积分方法揭示了一系列关于气体动力学欧拉系统适定性的令人不安的事实，特别是存在稠密的“病态”初始数据，使该问题有无穷多个物理解可接受的（熵）弱解。本文确定了具有以下性质的初始数据类：（a）它们产生熵剖面递增的弱解族；（b）这些解是“离散”的，即仅取有限个常数状态；（c）当时间趋于无穷时，这些解达到规定的终端熵剖面。
英文摘要
The method of Convex Integration has revealed a number of rather disturbing facts concerning well-posedness of the Euler system of gas dynamics. In particular, there is a dense set of "wild" initial data, for which the problem admits infinitely many physically admissible (entropy) weak solutions. We identify the class of initial data enjoying the following properties: (a) they give rise to a family of weak solutions with increasing entropy profiles; (b) the solutions are "discrete", meaning they attain only a finite number of constant states; (c) the solutions reach a prescribed terminal entropy profile when time goes to infinity.
