论文标题
离散klein-gordon方程的急剧衰减估计值
Sharp time decay estimates for the discrete Klein-Gordon equation
论文作者
论文摘要
我们建立了在立方晶格上的klein-gordon方程式的急剧衰减估计，$ d = 2,3,4 $。 $ \ ell^1 \ to \ ell^{\ infty} $分散衰减率为$ | t |^{ - 3/4} $ for $ d = 2 $，$ d = 2 $，$ | t |^{ - 7/6} $ for $ d = 3 $ d = 3 $和$ | t |这些衰减率比Kevrekidis和Stefanov（2005）的猜想要快。证明依赖于振荡性积分估计，并通过对相关相函数的奇异性进行详细分析。我们还证明了Strichartz的新估计，并讨论了非线性PDE和光谱理论的应用。
We establish sharp time decay estimates for the the Klein-Gordon equation on the cubic lattice in dimensions $d=2,3,4$. The $\ell^1\to\ell^{\infty}$ dispersive decay rate is $|t|^{-3/4}$ for $d=2$, $|t|^{-7/6}$ for $d=3$ and $|t|^{-3/2}\log|t|$ for $d=4$. These decay rates are faster than conjectured by Kevrekidis and Stefanov (2005). The proof relies on oscillatory integral estimates and proceeds by a detailed analysis of the the singularities of the associated phase function. We also prove new Strichartz estimates and discuss applications to nonlinear PDEs and spectral theory.
