Regular hyperbolicity, dominant energy condition and causality for Lagrangian theories of maps
Regular hyperbolicity, dominant energy condition and causality for Lagrangian theories of maps
复制标题
拉格朗日地图理论的正则双曲性、主导能量条件和因果关系
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
W. Wong
中科院分区：
文献类型：
--
作者：
W. Wong
本文的目标有三个方面。首先是阐明拉格朗日场论的主导能量条件和双曲性之间的联系。第二，进一步分析了Skyrme模型双曲性的破坏，改进了Crutchfield和Bell的结果，并与Gibbons的结果进行了比较，给出了Skyrme模型动力学问题的局部适定性结果。第三是为相对论界提供一个关于赫里斯托杜卢正则双曲性框架的简短总结。在此过程中，证明了关于映射的拉格朗日理论的支配能量条件的一般定理，以及关于这些映射的双曲性的几个结果。
The goal of this paper is threefold. First is to clarify the connection between the dominant energy condition and hyperbolicity properties of Lagrangian field theories. Second is to provide further analysis on the breakdown of hyperbolicity for the Skyrme model, sharpening the results of Crutchfield and Bell and comparing against a result of Gibbons, and provide a local well-posedness result for the dynamical problem in the Skyrme model. Third is to provide a short summary of the framework of regular hyperbolicity of Christodoulou for the relativity community. In the process, a general theorem about dominant energy conditions for Lagrangian theories of maps is proved, as well as several results concerning hyperbolicity of those maps.