论文标题
在无效条件下2D Wave-Klein-Gordon耦合系统的渐近行为
Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition
论文作者
论文摘要
我们研究了具有半线性零非线性$ q_0 $和$ q_ {αβ} $的2D耦合波 - klein-gordon系统。主要结果指出，如果在某些加权的Sobolev空间中，不一定具有紧凑的支持，那么对2D耦合系统的解决方案存在于全球全球，并且我们还显示了解决方案的最佳时间衰减。 主要的困难在于波浪的缓慢衰减性质和两个空间维度的klein-gordon组件，此外，由于存在无Q_0 $的存在，这会出现额外的困难，这与klein-gordon方程不兼容。为了克服困难，需要对零形式的结构进行新的观察$ q_0 $。
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities $Q_0$ and $Q_{αβ}$. The main result states that the solution to the 2D coupled systems exists globally provided that the initial data are small in some weighted Sobolev space, which do not necessarily have compact support, and we also show the optimal time decay of the solution. The major difficulties lie in the slow decay nature of the wave and the Klein-Gordon components in two space dimensions, in addition, extra difficulties arise due to the presence of the null form $Q_0$ which is not of divergence form and is not compatible with the Klein-Gordon equations. To overcome the difficulties, a new observation for the structure of the null form $Q_0$ is required.
