Nonlinear modulational instabililty of the Stokes waves in 2d full water waves
arXiv:2012.15071
Abstract
The well-known Stokes waves refer to periodic traveling waves under the gravity at the free surface of a two dimensional full water wave system. In this paper, we prove that small-amplitude Stokes waves with infinite depth are nonlinearly unstable under long-wave perturbations. Our approach is based on the modulational approximation of the water wave system and the instability mechanism of the focusing cubic nonlinear Schrödinger equation.
References in corpus (12)
- Nonlinear Modulational Instability of Dispersive PDE Models
- A blow-up criteria and the existence of 2d gravity water waves with angled crests
- On a class of self-similar 2D surface water waves
- A Priori Estimates for Two-Dimensional Water Waves with Angled Crests
- Long-term regularity of 3D gravity water waves
- Two dimensional gravity waves at low regularity I: Energy estimates
- The quartic integrability and long time existence of steep water waves in 2D
- Well-posedness of the free boundary hard phase fluids in Minkowski background and its Newtonian limit
- On the lifespan of three-dimensional gravity water waves with vorticity
- On the transition of the Rayleigh-Taylor instability in 2d water waves
- Justification of Peregrine soliton from full water waves
- The Benjamin-Feir instability in the infinite depth