A globally smooth solution to the relativistic string equation

2021/08/31 by Wang, Jinhua, Wei, Changhua · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2108.13644

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.

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