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 Luli et al. (Adv. Math. 329: 174–188, 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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Acknowledgements
J.W. is supported by NSFC (Grant Nos. 12271450, 11871408). C.W. is supported by is partially supported by the Outstanding Youth Fund of Zhejiang Province (Grant No. LR22A010004) and the NSFC (Grant Nos. 12071435, 11871212).
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Wang, J., Wei, C. A Globally Smooth Solution to the Relativistic String Equation. J Geom Anal 33, 205 (2023). https://doi.org/10.1007/s12220-023-01258-1
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DOI: https://doi.org/10.1007/s12220-023-01258-1