标题： 椭圆系统的流的长时间存在性 显示英文标题

标题： Long Time Existence of A Flow of Elliptic Systems

摘要： 对于定义在黎曼曲面上的椭圆系统，Liouville系统和Toda系统代表了两种著名的类别，它们表现出截然不同的解结构。 多年来，这些系统的存在性结果突显了由于其独特的解结构而产生的差异。 在本工作中，我们旨在构造一种单调熵形式，并建立抛物系统流的长期存在性。 根据我们的主要定理，我们可以证明一些广泛类别的椭圆系统的存在性结果，包括Liouville系统和Toda系统。 我们的结果的强度进一步得到了证实，因为不需要关于黎曼曲面的拓扑信息，也不需要假设系数函数的正下界。 显示英文摘要

摘要： For elliptic systems defined on Riemann surfaces, Liouville and Toda systems represent two well-known classes exhibiting drastically different solution structures. Over the years, existence results for these systems have highlighted discrepancies due to their unique solution structures. In this work, we aim to construct a monotone entropy form and establish the long-term existence of a flow of parabolic systems. As a result of our main theorem, we can prove existence results for some broad classes of elliptic systems, including both Liouville and Toda systems. The strength of our results is further underscored by the fact that no topological information about the Riemann surfaces is required and no positive lower bound of coefficient functions is postulated.