Title: A globally smooth solution to the relativistic string equation Show Chinese title

Title: 相对论弦方程的全局光滑解

Abstract: We prove the global existence of smooth solution to the relativistic string equation in a class of data that is not small. Our solution admits the feature that the right-travelling wave can be large and the left-travelling wave is sufficiently small, and vice versa. In particular, the large-size solution exists in the whole space, instead of a null strip arising from the short pulse data. This generalizes the result of Liuli-Yang-Yu (Adv. Math. 2018) to the quasilinear setting with non-small data. In addition, in our companion paper, we are able to show the global solution here can also be seen as the non-small perturbations of the plane wave solutions. Show Chinese abstract

Abstract: 我们证明了在非小数据类中相对论弦方程的光滑解的全局存在性。 我们的解具有右行波可以很大而左行波足够小，反之亦然的特点。 特别是，大尺寸解存在于整个空间中，而不是由短脉冲数据引起的零带中。 这将Liuli-Yang-Yu（Adv. Math. 2018）的结果推广到非小数据的拟线性情形。 此外，在我们的配套论文中，我们能够证明这里的全局解也可以看作是平面波解的非小扰动。