A simple justification of the singular limit for equatorial shallow‐water dynamics
A simple justification of the singular limit for equatorial shallow‐water dynamics
复制标题
赤道浅水动力学奇异极限的简单论证
DOI：
--
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
A. Majda
中科院分区：
文献类型：
--
作者：
Alexandre Dutrifoy;S. Schochet;A. Majda
赤道浅水方程在低弗劳德数下形成一个具有大变系数项的对称双曲方程组。虽然经典的Klainerman-Majda奇异极限理论不包括这样的系统，但前两位作者最近证明了解一致存在，并且当高度和弗劳德数趋于0时收敛于长波方程的解。他们的证明利用了方程的特殊结构，通过将解展开为一系列抛物柱面函数。在这里，根据经典理论的精神，提出了一个稍微推广的简单证明。© 2008 Wiley Periodicals，Inc.
The equatorial shallow‐water equations at low Froude number form a symmetric hyperbolic system with large variable‐coefficient terms. Although such systems are not covered by the classical Klainerman‐Majda theory of singular limits, the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long‐wave equations as the height and Froude number tend to 0. Their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions. A simpler proof of a slight generalization is presented here in the spirit of the classical theory. © 2008 Wiley Periodicals, Inc.