论文标题
关于双曲线空间上NLS的高低方法
On the high-low method for NLS on the hyperbolic space
论文作者
论文摘要
在本文中，我们首先证明，在$ H^S（\ Mathbb {h}^2）$中，在二维双曲线空间上使用非线性schrödinger方程式散落，当$ h^s（\ mathbb {h}^2）$散布时，当$ s> \ s> \ frac {3} {4} {4} $时散布。然后，我们将结果扩展到订单$ p> 3 $的非平局。结果是通过在双曲线环境中扩展了高低的波尔加恩的高低方法，并使用第一作者和Ionescu证明的Morawetz类型估计值证明了结果。
In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in $H^s(\mathbb{H}^2)$ is globally well-posed and scatters when $s > \frac{3}{4}$. Then we extend the result to nonlineraities of order $p>3$. The result is proved by extending the high-low method of Bourgain in the hyperbolic setting and by using a Morawetz type estimate proved by the first author and Ionescu.
