Schwarzschild时空中相对论弦方程整体光滑解的存在性
The global existence of smooth solutions of relativistic string equations in the Schwarzschild space-time
摘要：
本文研究相对论性弦在史瓦西时空中的运动。作为一般框架，我们首先分析了p维扩展物体在一般包络时空（N; ~g）中运动的基本方程，该包络时空是一个给定的洛伦兹流形，然后详细研究了相对论弦在史瓦西时空中运动的方程所具有的有趣性质.在此基础上，在适当的假设下，我们证明了Schwarzschild时空中相对论性小弧长弦运动方程Cauchy问题整体光滑解的存在性。
英文摘要：
This paper concerns the motion of relativistic strings in the Schwarzschild space-time. As a general framework, we first analyze the basic equations for the motion of a p-dimensional extended object in a general enveloping space-time (N; ~g), which is a given Lorentzian manifold, and then particularly investigate the interesting properties enjoyed by the equations for the motion of relativistic strings in the Schwarzschild space-time. Based on this, under suitable assumptions we prove the global existence of smooth solutions of the Cauchy problem for the equations for the motion of relativistic strings with small arc length in the Schwarzschild space-time.
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