论文标题
1D立方NLS的新的关键解决方案
A new class of critical solutions for 1D cubic NLS
论文作者
论文摘要
本文的目的是证明存在一类新的1D立方NLS解决方案，其中具有与狄拉克群众总和，关键规律性$ f（l^\ infty）$相关的初始数据，并且属于任何$ s <-1/2 $的$ \ dot h^s $。此问题是由于缺乏临界规则性初始条件的结果，也是由于对二项制流量近似的涡旋细丝动力学的研究而引起的。我们的结果是基于散射方法，在执行伪符号的转换以及对振荡积分的良好估计之后。
The aim of this article is to prove the existence of a new class of solutions of 1D cubic NLS with an initial data related to a sum of Dirac masses, of critical regularity $F(L^\infty)$, and belonging to $\dot H^s$ for any $s <-1/2$. This problem is motivated by the lack of result for critical regularity initial condition, and also by the study of the vortex filaments dynamics approximated by the binormal flow. Our result is based on a scattering approach, after performing a pseudo-conformal transformation, and on fine estimations of oscillatory integrals.
