【摘要】 本文我们提出—类交叉强制变分方法来研究二维空间中的Klein-Gordon-Zakharov系统的整体解.首先,通过构造交叉强制变分问题,建立发展流的交叉不变流形,得到所研究系统解爆破和整体存在的一个最佳条件.其次,利用这个结论,我们回答了如下问题:当初值为多小时,所研究系统的整体解存在.更多还原

【Abstract】 In this paper,we present a cross-constrained variational approach to study the global solutions of the Klein-Gordon-Zakharov system in two space dimensions.By constructing a type of cross constrained variational problem and establishing so-called cross- invariant manifolds of the evolution flow,we first derive a sharp threshold of global existence and blowup,then we answer the question that how small the initial data are for the global solutions to exist.更多还原