耦合非线性Klein-Gordon方程组的整体解

Global Solution for a Coupled Nonlinear Klein-Gordon System

研究二维空间中一类耦合非线性Klein-Gordon方程组的整体解.首先,通过构造交叉强制变分问题且建立发展流的交叉不变流形,得到了该方程组解爆破和整体存在的一个最佳条件.然后利用尺度变换讨论证明了当初值为多小时,该方程组的整体解存在.

The global solution for a coupled nonlinear Klein-Gordon system in two space dimensions is studied.First,a sharp threshold of blowup and global existence for the system is obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow.Then the result of how small the initial data are for which the solution of the system exists globally is proved by using the scaling argument.