论文标题
关于立方四阶方程的衰减特性
On the decay property of the cubic fourth-order Schrödinger equation
论文作者
论文摘要
在这篇简短的论文中，我们证明了在$ \ mathbb {r}^d $（$ 5 \ leq d \ leq 8 $）上，立方四阶方程（4NLS）的解决方案享受与线性解决方案相同的（尖端）衰减属性。该结果通过基于相应的全局结果pausader \ cite {pau1}的bootstrap参数证明。该结果可以扩展到具有散射渐近学的更通用的分散方程（包括更多的4NLS模型）。
In this short paper, we prove that the solution of the cubic fourth-order Schrödinger equation (4NLS) on $\mathbb{R}^d$ ($5 \leq d \leq 8$) enjoys the same (pointwise) decay property as its linear solution does. This result is proved via a bootstrap argument based on the corresponding global result Pausader \cite{Pau1}. This result can be extended to more general dispersive equations (including some more 4NLS models) with scattering asymptotics.
