Continuity and analyticity for a generalized two-component short pulse system

Shanshan Zheng; Li Yang; Shanshan Zheng; Li Yang

doi:10.3934/math.20251065

AIMS Mathematics

2025, Volume 10, Issue 10: 23958-23983. doi: 10.3934/math.20251065

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Continuity and analyticity for a generalized two-component short pulse system

Shanshan Zheng ^{1
,
,},
Li Yang ²

1.
College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
2.
School of Mathematical and Physical Sciences, Chongqing University of Science and Technology, Chongqing 401331, China

Received: 25 July 2025 Revised: 27 September 2025 Accepted: 10 October 2025 Published: 21 October 2025
MSC : 35B65, 35B10, 35M31, 35G25

In this paper, we first established the local well-posedness of the generalized short pulse system in the critical Besov space $ B_{2, 1}^{\frac{3}{2}}(\mathbb{T}) $, improving upon the local well-posedness result obtained in [S. Yu, X. Yin, J. Math. Anal. Appl., 475 (2019), 1427–1447]. We then proved that the solution map was Hölder continuous in $ B_{2, r}^{\mu}(\mathbb{T}) $. Finally, by a generalized Ovsyannikov theorem combined with fundamental properties of Sobolev-Gevrey spaces, we established the Gevrey regularity and analyticity of solutions and further obtained a lower bound of the lifespan and the continuity of the data-to-solution map.
- local well-posedness,
- Hölder continuous,
- Gevrey regularity and analyticity
Citation: Shanshan Zheng, Li Yang. Continuity and analyticity for a generalized two-component short pulse system[J]. AIMS Mathematics, 2025, 10(10): 23958-23983. doi: 10.3934/math.20251065

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Abstract

In this paper, we first established the local well-posedness of the generalized short pulse system in the critical Besov space $ B_{2, 1}^{\frac{3}{2}}(\mathbb{T}) $, improving upon the local well-posedness result obtained in [S. Yu, X. Yin, J. Math. Anal. Appl., 475 (2019), 1427–1447]. We then proved that the solution map was Hölder continuous in $ B_{2, r}^{\mu}(\mathbb{T}) $. Finally, by a generalized Ovsyannikov theorem combined with fundamental properties of Sobolev-Gevrey spaces, we established the Gevrey regularity and analyticity of solutions and further obtained a lower bound of the lifespan and the continuity of the data-to-solution map.

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