Compressible steady water waves

Abba Ramadan; Samuel Walsh

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arXiv · 2610.01883

Compressible steady water waves

Abba Ramadan·Samuel Walsh

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Abstract

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.

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BibTeX RIS

Abba Ramadan, Samuel Walsh. 2026-10-01. Compressible steady water waves. https://arxiv.org/abs/2610.01883

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