论文标题
波 - 克莱因 - 戈登模型的保形倍正型能的界限
Boundedness of the conformal hyperboloidal energy for a wave-Klein-Gordon model
论文作者
论文摘要
我们考虑了一个模型的全局演化问题，该模型将非线性波方程和非线性klein-gordon方程组合在一起，并由Lefloch和Y. Ma和Q. Wang独立引入。通过重新访问倍曲面叶面方法，我们确定溶液的加权能量（几乎）始终存在。证明中的新成分是由两个共形变换定义的分数摩拉维兹能量估计值（对于系统的波分量）的层次结构。这些能量估计的最佳情况对应于使用缩放矢量场作为波分量的乘数。
We consider the global evolution problem for a model which couples together a nonlinear wave equation and a nonlinear Klein-Gordon equation, and was independently introduced by LeFloch and Y. Ma and by Q. Wang. By revisiting the Hyperboloidal Foliation Method, we establish that a weighted energy of the solutions remains (almost) bounded for all times. The new ingredient in the proof is a hierarchy of fractional Morawetz energy estimates (for the wave component of the system) which is defined from two conformal transformations. The optimal case for these energy estimates corresponds to using the scaling vector field as a multiplier for the wave component.
