论文标题
上下$ l^2 $ -DECAY界限，用于一类衍生品非线性schrödinger方程
Upper and lower $L^2$-decay bounds for a class of derivative nonlinear Schrödinger equations
论文作者
论文摘要
我们考虑了在一个空间维度中具有弱耗散结构的立方导数非线性schrödinger方程的初始值问题。我们表明，小型数据解决方案在$ o（（\ log t）^{ - 1/4}）$中腐烂，$ l^2 $ as $ t \ to +\ to +\ infty $。此外，我们发现，通过给出较低的相同订单估算值，这一$ l^2 $ - 订单是最佳的。
We consider the initial value problem for cubic derivative nonlinear Schrödinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as $t\to +\infty$. Furthermore, we find that this $L^2$-decay rate is optimal by giving a lower estimate of the same order.
