论文标题
3D散焦，立方schrödinger方程的全球适应性和散射
Global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation
论文作者
论文摘要
在本文中，我们研究了3D散热器，立方schrödinger方程的全球体系良好和散射。最近，Dodson [Arxiv：2004.09618]在关键的Sobolev空间$ \ dot {W}^{11/7,7/6} $中研究了全球范围良好。在本文中，我们的目的是表明，如果初始数据属于$ \ dot h^\ frac12 $，以保证当地的存在，那么一些亚临界的额外弱空间就足以证明全球范围。更准确地说，我们证明，如果初始数据属于$ \ dot {h}^{1/2} \ cap \ dot {w}^{s，1} $，则为$ 12/13 <s \ s \ leqslant 1 $，那么对应的解决方案存在全球和散射。
In this paper, we study the global well-posedness and scattering of 3D defocusing, cubic Schrödinger equation. Recently, Dodson [arXiv:2004.09618] studied the global well-posedness in a critical Sobolev space $\dot{W}^{11/7,7/6}$. In this paper, we aim to show that if the initial data belongs to $\dot H^\frac12$ to guarantee the local existence, then some extra weak space which is subcritical, is sufficient to prove the global well-posedness. More precisely, we prove that if the initial data belongs to $\dot{H}^{1/2}\cap \dot{W}^{s,1}$ for $12/13<s \leqslant 1$, then the corresponding solution exists globally and scatters.
