【摘要】 本文用变分法研究三维空间中一类耦合非线性Klein-Gordon方程组.通过构造一类交叉强制变分问题,并建立对应于该方程组的发展流的交叉不变流形,得到该方程组解爆破和整体存在的最佳条件,并证明了当初值为多小时,该方程组的整体解存在这个问题.更多还原

【Abstract】 In this paper,a variational approach is first presented to study a class of coupled nonlinear Klein-Gordon equations in three space dimensions.By constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow,a sharp threshold for blowing up and global existence is obtained and how small the initial data are for the global solutions to exist is shown.更多还原