Affiliation:
1. School of Mathematics, Hunan Institute of Science and Technology 1 , Yueyang 414006, Hunan, China
2. School of Mathematics and Statistics, Central South University 2 , Changsha 410083, Hunan, China
Abstract
In this paper, benefited some ideas of Wang [J. Geom. Anal. 33, 18 (2023)] and Dufera et al. [J. Math. Anal. Appl. 509, 126001 (2022)], we investigate persistence of spatial analyticity for solution of the higher order nonlinear dispersive equation with the initial data in modified Gevrey space. More precisely, using the contraction mapping principle, the bilinear estimate as well as approximate conservation law, we establish the persistence of the radius of spatial analyticity till some time δ. Then, given initial data that is analytic with fixed radius σ0, we obtain asymptotic lower bound σ(t)≥c|t|−12, for large time t ≥ δ. This result improves earlier ones in the literatures, such as Zhang et al. [Discrete Contin. Dyn. Syst. B 29, 937–970 (2024)], Huang–Wang [J. Differ. Equations 266, 5278–5317 (2019)], Liu–Wang [Nonlinear Differ. Equations Appl. 29, 57 (2022)], Wang [J. Geom. Anal. 33, 18 (2023)] and Selberg–Tesfahun [Ann. Henri Poincaré 18, 3553–3564 (2017)].
Funder
Scientific Research Fund of Hunan Provincial Education Department
Hunan Province Graduate Research Innovation Project
Research and Innovation Team of Hunan Institute of Science and Technology
NNSF of China
NSFC-RGC Joint Research