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The Cauchy problem for fractional Camassa–Holm equation in Besov space
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.nonrwa.2021.103348 Lili Fan , Hongjun Gao , Junfang Wang , Wei Yan
中文翻译:
Besov空间中分数阶Camassa–Holm方程的Cauchy问题
更新日期:2021-05-06
Nonlinear Analysis: Real World Applications ( IF 1.8 ) Pub Date : 2021-05-06 , DOI: 10.1016/j.nonrwa.2021.103348 Lili Fan , Hongjun Gao , Junfang Wang , Wei Yan
In this paper, we consider the fractional Camassa–Holm equation modeling the propagation of small-but-finite amplitude long unidirectional waves in a nonlocally and nonlinearly elastic medium. First, we establish the local well-posedness in Besov space with for and for . Then, with a given analytic initial data, we establish the analyticity of the solutions in both variables, globally in space and locally in time. Finally, we give a blow-up criterion.
中文翻译:
Besov空间中分数阶Camassa–Holm方程的Cauchy问题
在本文中,我们考虑了分数Camassa-Holm方程,该方程对小但有限振幅的长单向波在非局部和非线性弹性介质中的传播进行建模。首先,我们建立Besov空间中的局部适定性 和 为了 和 为了 。然后,利用给定的分析初始数据,我们建立了两个变量(空间上全局和时间上局部)的解析性。最后,我们给出了爆炸标准。