论文标题
洛伦兹仪表中的麦克斯韦·克莱恩·戈登方程的无限散射
Scattering from Infinity of the Maxwell Klein Gordon Equations in Lorenz Gauge
论文作者
论文摘要
我们证明了从洛伦兹仪表中满足弱的无效条件的麦克斯韦·克莱因·戈登方程的无穷大的散射数据的全球存在。 Lorenz仪表中Maxwell Klein Gordon方程的渐近方法显示出像零无限的波浪一样的波动，并且在Arxiv中对及时的无限无限的均匀性：1803.11086，并以辐射场表示，因此我们的散射数据将以后卫问题的辐射场形式给出。我们在Arxiv：1803.11086中提供了渐近学结果的完善，然后利用这种改进，我们找到了一个全局解决方案，该解决方案可以在无穷大处获得规定的散射数据。我们的工作始于[22]的方法，并且更加精致，因为它涉及衍生品较少的非线性。我们的结果对应于散射理论中的“散射状态的存在”。证明的方法依赖于散射数据的合适构造近似解决方案，加权的共形莫拉维斯能量估计以及Hardy不平等的时空版本。
We prove global existence backwards from the scattering data posed at infinity for the Maxwell Klein Gordon equations in Lorenz gauge satisfying the weak null condition. The asymptotics of the solutions to the Maxwell Klein Gordon equations in Lorenz gauge were shown to be wave like at null infinity and homogeneous towards timelike infinity in arXiv:1803.11086 and expressed in terms of radiation fields, and thus our scattering data will be given in the form of radiation fields in the backward problem. We give a refinement of the asymptotics results in arXiv:1803.11086, and then making use of this refinement, we find a global solution which attains the prescribed scattering data at infinity. Our work starts from the approach in [22] and is more delicate since it involves nonlinearities with fewer derivatives. Our result corresponds to "existence of scattering states" in the scattering theory. The method of proof relies on a suitable construction of the approximate solution from the scattering data, a weighted conformal Morawetz energy estimate and a spacetime version of Hardy inequality.
