论文标题
关于底部不均匀的浅水方程的评论
Remarks on dispersion-improved shallow water equations with uneven bottom
论文作者
论文摘要
结果表明，为了改善其分散性能，渐近（boussinesq状）浅水近似（Boussinesq状）浅水近似的修改可能会导致底部不均匀（即，实际上没有改善分散体）。还表明，当水深度不恒定时，这些修饰会导致不足的方程。这些缺点用（完全非线性的，弱分散的）serre方程说明。我们还得出渐近一致，良好的修改后的Serre方程，具有改进的分散性能，可用于底部的恒定斜率。
It is shown that asymptotically consistent modifications of (Boussinesq-like) shallow water approximations, in order to improve their dispersive properties, can fail for uneven bottoms (i.e., the dispersion is actually not improved). It is also shown that these modifications can lead to ill-posed equations when the water depth is not constant. These drawbacks are illustrated with the (fully nonlinear, weakly dispersive) Serre equations. We also derive asymptotically consistent, well-posed, modified Serre equations with improved dispersive properties for constant slopes of the bottom.
