Blow-up, global existence and propagation speed for a modified Camassa–Holm equation both dissipation and dispersion in $$H^{s,p}(\mathbb {R})$$
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Abstract
In this essay, we investigate the blow-up scenario, global solution and propagation speed for a modified Camassa–Holm (MCH) equation both dissipation and dispersion in Sobolev space \(H^{s,p} (\mathbb {R})\) , \(s\ge 1\) , \(p\in (1,\infty )\) . First of all, by the mathematical induction of index s, we establish the precise blow-up criteria, which extends the result obtained by Gui et al. in article (Comm Math Phys 319: 731–759, 2013). Secondly, we derive the global existence of the strong solution of MCH equation both dissipation and dispersion. Eventually, the propagation speed of the equation is studied when the initial data are compactly supported.
在$$H^{s,p}(\mathbb {R})$$中同时耗散和分散的修正卡马萨-霍尔姆方程的沸腾、全局存在性和传播速度
Abstract 在这篇文章中，我们研究了修正的卡马萨-霍尔姆（MCH）方程在Sobolev空间（H^{s,p} (\mathbb {R})\) 中既耗散又分散的炸毁情形、全局解和传播速度。, （s\ge 1\ ） , （p\in (1,\infty )\ ） 。首先，通过索引 s 的数学归纳，我们建立了精确的炸毁标准，这扩展了桂等人在文章（Comm Math Phys 319: 731-759, 2013）中得到的结果。其次，我们推导出了 MCH 方程耗散和离散强解的全局存在性。最后，研究了方程在初始数据紧凑支撑时的传播速度。
本文章由计算机程序翻译，如有差异，请以英文原文为准。
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