一类耦合非线性波相互作用模型初值问题解的全局适定性

Global Well-Posedness of Soluitions to the Initial Value Problem for a Coupled Nonlinear Model of Wave Interaction

本文利用Banach不动点原理对Hirota与Satsuma提出的一类耦合非线性波相互作用模型之初值问题进行了讨论，得到其解在Hs（R）XHs（R），S≥1，中的全局运定性。

Here is established the global well -posedness of solutions in Hs (R)XHs(R), S≥1 of the intial value problem for a coupled nonlinear model describing the interaction of two dispersive waves. The main idea comes from Kato's theory for nonlinear hyperbolic equations and results of singular integrals, which permits us ta use Banach's fixed point principle. The key point is the setup of the global a priori estimates for the solutions, which plays an important role in the derivation of global results. The present paper is a reversion of the author's former report.