论文标题
关于$ l^2 $的修改后的KDV方程式的良好的评论
A remark on the well-posedness of the modified KdV equation in $L^2$
论文作者
论文摘要
我们在焦点和散热情况下研究了实线和圆的实价修改的KDV方程。通过采用Killip和Vişan（2019）引入的通勤流的方法，我们证明了$ H^{s} $中的全球适应性，以$ 0 \ leq S <\ tfrac {1} {2} {2} $。在这条线上，我们展示了Harrop-Griffiths，Killip和Vişan（2020）最近的论文中的论点如何在较高的规律性制度中简化$ S \ geq 0 $。在圆圈上，我们提供了$ l^2 $的尖锐全球适合度的替代证明，这是由于Kappeler和Topalov（2005），并且还将其扩展到大型DATA Focusing Case。
We study the real-valued modified KdV equation on the real line and the circle, in both the focusing and the defocusing case. By employing the method of commuting flows introduced by Killip and Vişan (2019), we prove global well-posedness in $H^{s}$ for $0\leq s<\tfrac{1}{2}$. On the line, we show how the arguments in the recent paper by Harrop-Griffiths, Killip, and Vişan (2020) may be simplified in the higher regularity regime $s\geq 0$. On the circle, we provide an alternative proof of the sharp global well-posedness in $L^2$ due to Kappeler and Topalov (2005), and also extend this to the large-data focusing case.
