论文标题
周期性广义korteweg-de Vries方程的平滑和生长绑定
Smoothing and growth bound of periodic generalized Korteweg-de Vries equation
论文作者
论文摘要
对于具有多项式非线性的通用KDV模型，我们在$ h^s $中建立非线性平滑属性，以$ s> \ frac {1} {2} $。只要$ h^1 $ norm不会在有限的时间内爆炸，这种平滑效果仍在全球范围内持续。更具体地说，我们表明，解决方案的非线性部分的翻译获得了$ \ min（2S-1,1） - $ s> \ frac {1} {2} $的$衍生物。遵循一种新的简单方法，即具有独立关注的新方法，我们确定，对于$ s> 1 $，$ h^s $ norm of Solution of Solution tos to $ \ langle t \ rangle^{s-1+} $如果$ h^1 $ norm norm是先验控制的。
For generalized KdV models with polynomial nonlinearity, we establish nonlinear smoothing property in $H^s$ for $s>\frac{1}{2}$. Such smoothing effect persists globally, provided that the $H^1$ norm does not blow up in finite time. More specifically, we show that a translate of the nonlinear part of the solution gains $\min(2s-1,1)-$ derivatives for $s>\frac{1}{2}$. Following a new simple method, which is of independent interest, we establish that, for $s>1$, $H^s$ norm of a solution grows at most by $\langle t\rangle^{s-1+}$ if $H^1$ norm is a priori controlled.
