论文标题
在两个维度上的whitham- boussinesq系统的长期存在
Long-time existence for a Whitham--Boussinesq system in two dimensions
论文作者
论文摘要
本文涉及一个二维的Whitham-Boussinesq系统建模不可压缩的流体层的表面波。我们证明，相关的cauchy问题对于低规律性的初始数据很适合，并且存在规模$ \ Mathcal o（1/\sqrtε）$，其中$ε> 0 $是测量波动幅度的浅表参数，以测量波动的平均深度。证明中的关键成分是频率润滑的色散和strichartz的估计，这些分散率取决于$ε$以及在某些strichartz规范中的双线性估计。
This paper is concerned with a two dimensional Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We prove that the associated Cauchy problem is well-posed for initial data of low regularity, with existence time of scale $\mathcal O(1/\sqrtε)$, where $ε>0$ is a shallowness parameter measuring the ratio of the amplitude of the wave to the mean depth of the fluid. The key ingredients in the proof are frequency loacalised dispersive and Strichartz estimates that depend on $ε$ as well as bilinear estimates in some Strichartz norms.
