Amplitude Bounds of Steady Rotational Water Waves
Abstract
Abstract. We consider classical steady water waves with a free surface, a flat bottom, and constant vorticity [Formula: see text]. In the adverse case [Formula: see text] we prove the first absolute upper bound on the amplitude, independent of the physical constants, provided that [Formula: see text] is sufficiently small. In any favorable case [Formula: see text] we present a new proof of such an absolute bound on the amplitude and prove that the amplitude tends to zero as [Formula: see text] tends to [Formula: see text].
Fields of Study & Subjects
Ocean Waves and Remote Sensing
Methane Hydrates and Related Phenomena
Coastal and Marine Dynamics
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 1812–1830
- Publication date
- 13 April 2026
- Language
- EN