论文标题
对于无效状态的准线性波方程的敏锐衰减
Generically sharp decay for quasilinear wave equations with null condition
论文作者
论文摘要
我们对无效条件的三维准电波方程感兴趣。在Klainerman \ cite {klainerman86}和Christodoulou \ Cite {ChristoDoulou86}的著名作品中证明了该模型的全球存在和衰减。在这项工作中，我们说明了在倍曲底上构成的初始数据的解决方案的确切渐近行为，并表明衰减速率$ v^{ - 1} u^{ - 1} $对于一组通用的初始数据是最佳的。
We are interested in the three-dimensional quasilinear wave equations with null condition. Global existence and pointwise decay for this model have been proved in the celebrated works of Klainerman \cite{Klainerman86} and Christodoulou \cite{Christodoulou86} for small smooth initial data. In this work, we illustrate the precise pointwise asymptotic behavior of the solutions for initial data posed on a hyperboloid and show that the decay rate $v^{-1}u^{-1}$ is optimal for a generic set of initial data.
