发表机构
University of Alabama; CONSERVE Center, Alabama Water Institute, The University of Alabama; University of Missouri（阿拉巴马大学; 阿拉巴马大学阿拉巴马水研究所CONSERVE中心; 密苏里大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过分岔方法，以马赫数为参数，从不可压缩解构造可压缩水波，涵盖周期波、孤立波及两相前驱波，并给出詹森-瑞利展开的严格版本。
AI 中文摘要
本文考虑小振幅和大振幅可压缩水波的存在性。这些波是二维自由边界等熵欧拉方程在恒定重力作用下且忽略表面张力效应的解。我们研究了真空下方的周期波和孤立波，以及渠道中两相问题的前驱型解。利用局部和全局分岔技术，我们从不可压缩解出发，将马赫数（在适当意义上定义）作为分岔参数，构造了这些波的大族。这给出了经典詹森-瑞利展开的严格版本，同时也提供了可能趋于跨声速流的解曲线。
英文摘要
In this paper, we consider the existence of small- and large-amplitude compressible water waves. These are solutions of the two-dimensional free boundary isentropic Euler equations subjected to a constant gravitational force and neglecting the effects of surface tension. We study periodic and solitary waves beneath vacuum as well as front-type solutions of the two-phase problem in a channel. Using local and global bifurcation techniques, we construct large families of these waves beginning at an incompressible solution and treating the Mach number (defined in a suitable sense) as the bifurcation parameter. This gives a rigorous version of the classical Janzen--Rayleigh expansion, but also furnishes solution curves that may limit to transsonic flow.
