论文标题
定期广义非线性schrödinger方程的非线性平滑
Non-linear Smoothing for the Periodic Generalized Non-linear Schrödinger Equation
论文作者
论文摘要
我们考虑定期的非线性schrödinger方程，其非线性由$ | u | u |^{p-1} u $ for Odd $ p> 1 $ in Dimension $ 1 $。我们首先确定非线性演化与线性演化的相位旋转之间的差异在于平滑的空间中。然后，我们研究了上述类型的非线性schrödinger方程的强制和降解，并建立了一个类似的平滑陈述，该陈述在全球范围内扩展。作为推论，我们在能量空间中为全球吸引子建立了存在和平滑度。
We consider the periodic non-linear Schrödinger equation with non-linearity given by $|u|^{p-1}u$ for odd $p > 1$ in dimension $1$. We first establish that the difference between the non-linear evolution and a phase rotation of the the linear evolution is in a smoother space. We then study forced and damped defocusing non-linear Schrödinger equations of the above type and establish an analogous smoothing statement that extends globally in time. As a corollary we establish both existence and smootheness for global attractors in the energy space.
