论文标题
2D重力水波的长期规律性
Long-term regularity of 2D gravity water waves
论文作者
论文摘要
二维重力水波问题涉及不可压缩的液体的运动，占据了一半的2D空间，并在其自身的重力下流动。在本文中，我们研究了从小但非定位的初始数据演变的解决方案的长期规律性。 我们的主要结果是，如果初始数据的$ h^s $规范为$ε$，其中$ s \ gg 1 $和$ε\ ll 1 $ 1 $，那么该方程至少在与$ε^{ - 4} $成比例成比例的时间内得到很好的量，在$ε^{ - 3} $ lifespan上获得了改进，从而在\ cite中获得了改进。我们还研究了水波，并显示了寿命，弥合了非周期性波和波浪之间的缝隙，其周期为1。
The two dimensional gravity water wave problem concerns the motion of an incompressible fluid occupying half the 2D space and flowing under its own gravity. In this paper we study long-term regularity of solutions evolving from small but non-localized initial data. Our main result is that if the $H^s$ norm of the initial data is $ε$, where $s \gg 1$ and $ε\ll 1$, then the equation is wellposed at least for a time proportional to $ε^{-4}$, improving on the $ε^{-3}$ lifespan obtained in \cite{BeFePu,Wu2DL}. We also study period water waves and show a lifespan bridging the gap between non-periodic waves and waves with a period of 1.
