Minkowski空间上带电标量场的全局稳定性
Global Stability for Charged Scalar Fields on Minkowski Space
摘要：
本文证明了在（3+1）维Minkowski空间中，在一定的规范协变加权索伯列夫空间中，当初值较小时，电荷标量场方程（又称无质量Maxwell-Klein-Gordon方程）是全局稳定的.这些空间可以被选择为相对于方程的齐次性几乎是尺度不变的。这一结果对非零电荷的初始数据是有效的，初始数据在类空无穷远处也是非平稳的。证明方法是一个张量几何方法，它是基于一个特定的家庭加权双线性L2时空估计。
英文摘要：
We prove that the charge-scalar field (also known as the massless Maxwell-Klein-Gordon) equations are globally stable on (3+1) dimensional Minkowski space for small initial data in certain gauge covariant weighted Sobolev spaces. These spaces can be chosen as to be almost scale invariant with respect to the homogeneity of the equations. This result is valid for initial data with non-zero charge that is also non-stationary at space-like infinity. The method of proof is a tensor-geometric approach which is based on a certain family of weighted bilinear L2 space-time estimates.
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