This paper is devoted to a new integrable two-component Novikov equation with Lax pairs and bi-Hamiltonian structures. Ons the one hand, based on a generalized Ovsyannikov type theorem, we prove the existence and uniqueness of solutions in the Gevrey–Sobolev spaces with the lower bound of the lifespan, and show the continuity of the data-to-solution map. On the other hand, we prove that the strong solutions maintain corresponding properties at infinity within its lifespan provided the initial data decay exponentially and algebraically, respectively.

中文翻译：

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关于一个新的可积二元诺维科夫方程的柯西问题

本文致力于一个新的具有 Lax 对和双​​哈密尔顿结构的可积二元诺维科夫方程。一方面，基于广义的 Ovsyannikov 类型定理，我们证明了具有寿命下界的 Gevrey-Sobolev 空间中解的存在性和唯一性，并展示了数据到解映射的连续性。另一方面，我们证明，如果初始数据分别呈指数和代数衰减，强解在其生命周期内在无穷远处保持相应的属性。