《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (12): 75-83.doi: 10.6040/j.issn.1671-9352.0.2023.505
高亚琴,王海权*,滕凯民
GAO Yaqin, WANG Haiquan*, TENG Kaimin
摘要: 利用具有抽象形式的Cauchy-Kovalevsky定理研究一个rotation-μ-Camassa-Holm方程Cauchy问题解的局部解析性,通过推广的Ovsyannikov定理,讨论一个rotation-Camassa-Holm方程Cauchy问题的解在某些Sobolev-Gevrey空间中的局部解析性,并给出解析解存在的时间区间。
中图分类号:
| [1] MOON B. Nonexistence of periodic peaked traveling wave solutions to a rotation μ-Camassa-Holm equation with Coriolis effect[J]. Nonlinear Analysis: Real World Applications, 2023, 70:103793. [2] GUI Guilong, LIU Yue, SUN Junwei. A nonlocal shallow-water model arising from the full water waves with the Coriolis effect[J]. Journal of Mathematical Fluid Mechanics, 2019, 21(2):27. [3] CAMASSA R, HOLM D D. An integrable shallow water equation with peaked solitons[J]. Physical Review Letters, 1993, 71(11):1661-1664. [4] XIAO Li, QI Xueyuan, LI Fengquan. Non-uniform dependence on initial data for the rotation-Camassa-Holm equation[J]. Journal of Mathematical Fluid Mechanics, 2022, 24(4):107. [5] GUO Yingying, YIN Zhaoyang. The Cauchy problem of the rotation Camassa-Holm equation in equatorial water waves[J]. Applicable Analysis, 2021, 100(12):2547-2563. [6] ZHANG Lei. Non-uniform dependence and well-posedness for the rotation-Camassa-Holm equation on the torus[J]. Journal of Differential Equations, 2019, 267(9):5049-5083. [7] KHESIN B, LENELLS J, MISIOŁEK G. Generalized Hunter-Saxton equation and the geometry of the group of circle diffeomorphisms[J]. Mathematische Annalen, 2008, 342(3):617-656. [8] BAOUENDI M S, GOULAOUIC C. Sharp estimates for analytic pseudodifferential operators and application to Cauchy problems[J]. Journal of Differential Equations, 1983, 48(2):241-268. [9] BAOUENDI M S, GOULAOUIC C. Remarks on the abstract form of nonlinear Cauchy-Kovalevsky theorems[J]. Communications in Partial Differential Equations, 1977, 2(11):1151-1162. [10] HIMONAS A A, MISIOŁEK G. Analyticity of the Cauchy problem for an integrable evolution equation[J]. Mathematische Annalen, 2003, 327(3):575-584. [11] FU Ying. A note on the Cauchy problem of a modified Camassa-Holm equation with cubic nonlinearity[J]. Discrete & Continuous Dynamical Systems-Series A, 2015, 35(5):2011-2039. [12] GALSTIAN A, YAGDJIAN K. Global solutions for semilinear Klein-Gordon equations in FLRW spacetimes[J]. Nonlinear Analysis: Theory, Methods & Applications, 2015, 113:339-356. [13] 朱长江,邓引斌. 偏微分方程教程[M]. 北京:科学出版社,2005:199-200. ZHU Changjiang, DENG Yinbin. An introduction to partial differential equations[M]. Beijing: Science Press, 2005:199-200. [14] YAN Kai, YIN Zhaoyang. Analytic solutions of the Cauchy problem for two-component shallow water systems[J]. Mathematische Zeitschrift, 2011, 269(3):1113-1127. [15] PALMIERI A, REISSIG M. A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass[J]. Journal of Differential Equations, 2019, 266(2/3):1176-1220. |
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