论文标题
与关键Sobolev数据的一般类别的hartree型非线性类别的立方dirac方程的散射
Scattering of cubic Dirac equations with a general class of Hartree-type nonlinearity for the critical Sobolev data
论文作者
论文摘要
最近，在某种程度上对非线性结构的特定假设进行了广泛的研究，对使用Hartree型非线性的Cutic Dirac方程的溶液的低指控性行为进行了广泛的研究。先前结果的关键方法是利用Yukawa潜力的非线性和衰减中的无效结构。在本文中，我们的目标是超越；我们研究了Cutic Dirac方程的强散射特性，具有相当一般的Hartree型非线性类别，该类别涵盖了库仑电势以及Yukawa电位和双线性形式，其中一个人无法使用特定的无效结构。作为直接应用程序，我们还获得了具有关键缩放sobolev数据的Boson-Star方程的散射。
Recently low-regularity behaviour of solutions to cubic Dirac equations with the Hartree-type nonlinearity has been extensively studied in somewhat a specific assumption on the structure of the nonlinearity. The key approach of previous results was to exploit the null structure in the nonlinearity and the decay of the Yukawa potential. In this paper, we aim to go beyond; we investigate the strong scattering property of cubic Dirac equations with quite a general class of the Hartree-type nonlinearity, which covers the Coulomb potential as well as the Yukawa potential, and the bilinear form, in which one cannot use the specific null structure. As a direct application, we also obtain the scattering for the boson-star equations with the scaling-critical Sobolev data.
