论文标题
关于周期性非线性schrödinger方程的全球适应性
On the global well-posedness for the periodic quintic nonlinear Schrödinger equation
论文作者
论文摘要
在本文中，我们考虑了Quintic的初始值问题，在$ \ bbb t^2 $上散发非线性schrödinger方程，并在关键的sobolev space $ h^{\ frac {\ frac {1} {2}}}}（\ bbb t^2）$中使用常规数据。我们表明，如果解决方案保持在$ h^{\ frac {1} {2}}}}}（\ bbb t^2）$中的最大间隔中，那么该解决方案在$ \ bbb t^2 $中的全球范围都很好。
In this paper, we consider the initial value problem for the quintic, defocusing nonlinear Schrödinger equation on $\Bbb T^2$ with general data in the critical Sobolev space $H^{\frac{1}{2}} (\Bbb T^2)$. We show that if a solution remains bounded in $H^{\frac{1}{2}} (\Bbb T^2)$ in its maximal interval of existence, then the solution is globally well-posed in $\Bbb T^2$.
