论文标题
有条件的大数据全球全球良好的狄拉克方程与hartree型非线性
Conditional large-data global well-posedness of Dirac equation with Hartree-type nonlinearity
论文作者
论文摘要
我们研究了在两个空间维度和三个空间维度中具有Yukawa型潜力的Hartree型非线性狄拉克方程的库奇问题。本文改善了我们以前的结果\ cite {chohlee，cholee};我们为具有一定条件的大数据建立了全球适应性和散射。首先，我们研究解决方案解决方案的长时间行为可以满足良好的控制，只要解决方案的特定分散规范是有限的。我们证明的关键依赖于修改以前论文中获得的多线性估计值。其次，我们通过利用Majorana条件来获得大型数据散射。
We study the Cauchy problems for the Hartree-type nonlinear Dirac equations with Yukawa-type potential in two and three spatial dimensions. This paper improves our previous results \cite{chohlee,cholee}; we establish global well-posedness and scattering for large data with a certain condition. Firstly we investigate the long-time behavior of solutions to the Dirac equation satisfies good control provided that a particular dispersive norm of solutions is bounded. The key of our proof relies on modifying multilinear estimates obtained in our previous papers. Secondly, we obtain large data scattering by exploiting the Majorana condition.
