On the Cauchy problem of a new integrable two-component Novikov equation
On the Cauchy problem of a new integrable two-component Novikov equation
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新可积二元诺维科夫方程的柯西问题
DOI：
10.1007/s00605-020-01430-7
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发表时间：
2020
影响因子：
0.9
通讯作者：
Huang Daiwen
中科院分区：
文献类型：
--
作者：
Mi Yongsheng;Huang Daiwen
本文研究了一个新的可积两分量Novikov方程、松弛对和双Hamilton结构。首先，利用Littlewood-Paley理论和迁移方程理论，建立了非齐次Besov空间中的局部适定性。然后，我们验证了该系统的爆破只发生在破碎波的形式。此外，与解析的初始数据，我们表明，它的解决方案是解析的两个变量，全球的空间和局部的时间。最后，我们证明了如果初始数据分别指数衰减和代数衰减，则系统的强解在其生命周期内在无穷远保持相应的性质。
This paper is devoted to a new integrable two-component Novikov equation, lax pairs and bi-Hamiltonian structures. Firstly, the local well-posedness in nonhomogeneous Besov spaces is established by using the Littlewood–Paley theory and transport equations theory. Then, we verify the blow-up that occurs for this system only in the form of breaking waves. Moreover, with analytic initial data, we show that its solutions are analytic in both variables, globally in space and locally in time. Finally, we prove that the strong solutions of the system maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.