Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits

Chenyun Luo; Junyan Zhang

doi:10.1016/j.jde.2026.114444

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arXiv · 2211.03600

Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits

Chenyun Luo·Junyan Zhang

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Abstract

We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and surface tension, and it is not assumed to be irrotational. We prove local well-posedness by combining a carefully designed approximate system and a hyperbolic approach, which allows us to avoid using Nash-Moser iteration. The energy estimates yield no regularity loss and are uniform in both Mach number and surface tension coefficient, provided the Rayleigh-Taylor sign condition is satisfied. We thus simultaneously obtain incompressible and zero surface tension limits. Moreover, we can drop the uniform boundedness (with respect to Mach number) on high-order time derivatives by applying the paradifferential calculus to the analysis of the free-surface evolution.

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Chenyun Luo, Junyan Zhang. 2026-04-26. Compressible Gravity-Capillary Water Waves with Vorticity: Local Well-Posedness, Incompressible and Zero-Surface-Tension Limits. https://doi.org/10.1016/j.jde.2026.114444

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