论文标题
klein-gordon方程的零质量问题：二次空相互作用
The zero mass problem for Klein-Gordon equations: quadratic null interactions
论文作者
论文摘要
我们在$ \ mathbb {r}^{3+1} $中学习一个在无效条件下的非线性耦合klein-gordon方程的系统，并且（可能消失的）质量在间隔$ [0，1] $中变化。我们的目标是三个折叠：1）我们要建立系统的全局良好性结果，该系统在质量参数方面是统一的； 2）我们希望在某个时间范围内获得解决方案溶液的统一型衰减结果，因为该解决方案更像是波浪分量（独立于质量参数），而解决方案则是klein-gordon分量，其因子在时间范围内的质量参数取决于质量参数； 3）当质量参数达到0时，Klein-Gordon系统的解决方案在某些意义上将解决方案收敛到相应的波系统。为了实现这些目标，我们将依靠时空的平坦和倍曲面叶面。
We study in $\mathbb{R}^{3+1}$ a system of nonlinearly coupled Klein-Gordon equations under null condition, with (possibly vanishing) mass varying in the interval $[0, 1]$. Our goal is three folds: 1) we want to establish the global well-posedness result to the system which is uniform in terms of the mass parameter; 2) we want to obtain unified pointwise decay result for the solution to the system, in the sense that the solution decays more like a wave component (independent of the mass parameter) in certain range of time, while the solution decays as a Klein-Gordon component with a factor depending on the mass parameter in the other part of the time range; 3) the solution to the Klein-Gordon system converges to the solution to the corresponding wave system in certain sense when the mass parameter goes to 0. In order to achieve these goals, we will rely on both the flat and the hyperboloidal foliation of the spacetime.
