论文标题
针对散射至关非线性的狄拉克方程的修改散射
The modified scattering for Dirac equations of scattering-critical nonlinearity
论文作者
论文摘要
在本文中，我们将Maxwell-DIRAC系统在零磁场下的3维度中考虑。我们证明了加权Sobolev类中的小解决方案的全球适合度和改良的散射。施加Lorenz量规条件（并乘坐Dirac投影操作员），它变成了一个dirac方程的系统，其hartree型非线性具有远距离电位为$ | x |^{ - 1} $。我们执行加权能量估计。在此过程中，我们必须处理源于狄拉克预测的各种共振函数。我们使用Germain-Masmoudi-Shatah的时空共鸣论点以及Spinorial Null结构。在途中，我们认识到一种远程相互作用，该远距离相互作用负责在修改后的散射语句中进行对数相校正。
In this paper, we consider the Maxwell-Dirac system in 3 dimension under zero magnetic field. We prove the global well-posedness and modified scattering for small solutions in the weighted Sobolev class. Imposing the Lorenz gauge condition, (and taking the Dirac projection operator), it becomes a system of Dirac equations with Hartree type nonlinearity with a long range potential as $|x|^{-1} $. We perform the weighted energy estimates. In this procedure, we have to deal with various resonance functions that stem from the Dirac projections. We use the spacetime resonance argument of Germain-Masmoudi-Shatah, as well as the spinorial null-structure. On the way, we recognize a long range interaction which is responsible for a logarithmic phase correction in the modified scattering statement.
