论文标题
周期性衍生品非线性schrödinger方程的生长结合和非线性平滑
Growth Bound and Nonlinear Smoothing for the Periodic Derivative Nonlinear Schrödinger Equation
论文作者
论文摘要
为全球Sobolev $ h^s（\ Mathbb t）$解决方案建立了一个多项式增长界限，以循环的衍生品非线性schrödinger方程为$ s> 1 $。这些边界是由于非线性平滑效应的结果而得出的，适用于周期性库奇问题的适当量规转换版本，根据该效果，其删除的线性零件的解决方案具有比与该解决方案相关的初始基准的更高的空间规律性。
A polynomial-in-time growth bound is established for global Sobolev $H^s(\mathbb T)$ solutions to the derivative nonlinear Schrödinger equation on the circle with $s>1$. These bounds are derived as a consequence of a nonlinear smoothing effect for an appropriate gauge-transformed version of the periodic Cauchy problem, according to which a solution with its linear part removed possesses higher spatial regularity than the initial datum associated with that solution.
