论文标题
散射在中间临界非统治不均匀NLS的基态下方
Scattering below the ground state for the intercritical non-radial inhomogeneous NLS
论文作者
论文摘要
我们考虑焦点不均匀的非线性schrödinger方程\ [i \ partial_t u +ΔU + | X |^{ - b} | $ 0 <b <\ min \ {\ tfrac {n} {2}，2 \} $和$ \ tfrac {4-2b} {n} {n} <α<\ tfrac {4-2b} {n-2b} {n-2} $。这些限制使方程式质量优势和能量肯定。我们将Farah-Guzmán和Miao-Murphy-Zheng的结果扩展到基态下方的散射，并具有一般的初始数据。
We consider the focusing inhomogeneous nonlinear Schrödinger equation \[ i\partial_t u + Δu + |x|^{-b}|u|^αu = 0\quad\text{on}\quad\mathbb{R}\times\mathbb{R}^N, \] with $N\geq 2$, $0<b<\min\{\tfrac{N}{2},2\}$, and $\tfrac{4-2b}{N}<α<\tfrac{4-2b}{N-2}$. These constraints make the equation mass-supercritical and energy-subcritical. We extend the results of Farah-Guzmán and Miao-Murphy-Zheng and prove scattering below the ground state with general initial data.
