Related papers: Low regularity solutions for gravity water waves I…
In this paper, we investigate the spectral stability of periodic traveling waves in the two dimensional gravity-capillary water wave problem. We derive a stability criterion based on an index function, whose sign determines the spectral…
Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…
A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…
Gerstner or trochoidal wave is the only known exact solution of the Euler equations for periodic surface gravity waves on deep water. In this Letter we utilize Zakharov's variational formulation of weakly nonlinear surface waves and,…
By establishing a sharp Strichartz estimate for the velocity and density, we prove the local well-posedness of solutions for the Cauchy problem of two-dimensional compressible Euler equations, where the initial velocity, density, and…
We consider gravity water waves in two space dimensions, with finite or infinite depth. Assuming some uniform scale invariant Sobolev bounds for the solutions, we prove local energy decay (Morawetz) estimates globally in time. Our result is…
This article is concerned with infinite depth gravity water waves with constant vorticity in two space dimensions. We consider this system expressed in position-velocity potential holomorphic coordinates. We show that, for low-frequency…
In certain models of conformal gravity, the propagation of gravitational waves is governed by a fourth order scalar partial differential equation. We study the initial value problem for a generalization of this equation, and derive a…
This paper studies the classical water wave problem with vorticity described by the Euler equations with a free surface under the influence of gravity over a flat bottom. Based on fundamental work \cite{ConstantinStrauss}, we first obtain…
We establish the full justification of a "Whitham-Green-Naghdi" system modeling the propagation of surface gravity waves with bathymetry in the shallow water regime. It is an asymptotic model of the water waves equations with the same…
In this paper we consider the 1D Green-Naghdi system over a nonflat bottom. This system describes the evolution of water waves over an uneven bottom in the shallow water regime in terms of the water depth $h$ and the horizontal velocity…
This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a…
In this paper we prove global regularity for the full water waves system in 3 dimensions for small data, under the influence of both gravity and surface tension. This problem presents essential difficulties which were absent in all of the…
This article is concerned with the incompressible, infinite depth water wave equation in two space dimensions, with gravity and constant vorticity but with no surface tension. We consider this problem expressed in position-velocity…
Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales…
The stability of Lattice Boltzmann Equations modelling Shallow Water Equations in the special case of reduced gravity is investigated theoretically. A stability notion is defined as applied in incompressible Navier-Stokes equations in…
We find exact static stringy solutions of Horava-Lifshitz gravity with the projectability condition but imposing the detailed balance condition near the UV fixed point, and propose a method on constraining the possible pattern of flows in…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
This paper is devoted to the well-posedness of the inhomogeneous nonlinear wave equations. By combining Strichartz estimates with the contraction mapping principle, we establish local and global well-posedness in the function spaces…
This paper considers two-dimensional stratified water waves propagating under the force of gravity over an impermeable flat bed and with a free surface. We prove the existence of a global continuum of classical solutions that are periodic…