论文标题
径向schrödinger方程的质量规律性几乎确定散射
Almost Sure Scattering at Mass Regularity for Radial Schrödinger Equations
论文作者
论文摘要
我们考虑径向非线性schrödinger方程$ i \ partial_tu +ΔU= | u |^| |^{p-1} u $ in Dimension $ d \ geqslant 2 $ for $ p \ in \ in \ weft（1,1+ \ frac \ frac {4} {4} $ l^2 _ {\ text {rad}} $，因此几乎每个初始数据都会产生唯一的全局解决方案。在径向情况下，伯克和托曼的工作的尺寸对应物。
We consider the radial nonlinear Schrödinger equation $i\partial_tu +Δu = |u|^{p-1}u$ in dimension $d\geqslant 2$ for $p\in \left(1,1+\frac{4}{d}\right]$ and construct a natural Gaussian measure $μ_0$ which support is almost $L^2_{\text{rad}}$ and such that $μ_0$ - almost every initial data gives rise to a unique global solution. Furthermore, for $p>1+\frac{2}{d}$ and $d\in\{2, \dots, 10\}$ the solutions constructed scatters in a space which is almost $L^2$. This paper can be viewed as the higher dimensional counterpart of the work of Burq and Thomann, in the radial case.
