论文标题
可压缩欧拉方程的非唯一可接受的弱解，在太空中具有紧凑的支持
Non-Unique Admissible Weak Solutions of the Compressible Euler Equations with Compact Support in Space
论文作者
论文摘要
本文关注的是，对于等质压缩的欧拉方程而言，存在针对凯奇问题的紧凑型解决方案。在一个以上的空间维度中，由de Lellis-székelyHidi和Chiodaroli开发的凸集成技术使我们能够证明从有限的时间间隔溶液中，从任何连续的可差异初始密度和适当构建的初始型界定力矩上开始，唯一的唯一性失败。特别是，这将Chiodaroli的工作从周期性的边界条件扩展到有限的域或整个空间。
This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis-Székelyhidi and Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta. In particular, this extends Chiodaroli's work from periodic boundary conditions to bounded domains or the whole space.
