论文标题
在三维产品空间上散发立方NLS的长时间动力学
Long time dynamics for defocusing cubic NLS on three dimensional product space
论文作者
论文摘要
在本文中，我们研究了在三维产品空间上使用立方NLS进行散热的长时间动力学。首先，我们将解耦方法应用于demeter \ cite {bd}以建立双线性strichartz估计。此外，我们证明了基于i-hethod和双线性估算的三维产品空间（$ h^s $，$ h^s $，$ h^s $，$ h^s $，$ s> \ frac {5} {6} $）的全球供应良好。最后，我们讨论了较高的Sobolev规范问题的增长，这与弱湍流现象紧密相关。
In this article, we study long time dynamics for defocusing cubic NLS on three dimensional product space. First, we apply the decoupling method in Bourgain-Demeter \cite{BD} to establish a bilinear Strichartz estimate. Moreover, we prove global well-posedness for defocusing, cubic NLS on three dimensional product space with rough initial data ($H^s$, $s>\frac{5}{6}$) based on I-method and the bilinear estimate. At last, we discuss the growth of higher Sobolev norm problem which is tightly linked to the weak turbulence phenomenon.
