Related papers: Strichartz Estimates for Water Waves
For the linear damped wave equation (DW), the $L^p$-$L^q$ type estimates have been well studied. Recently, Watanabe showed the Strichartz estimates for DW when $d=2,3$. In the present paper, we give Strichartz estimates for DW in higher…
We prove global smoothing and Strichartz estimates for the Schroedinger, wave, Klein-Gordon equations and for the massless and massive Dirac systems, perturbed with singular electromagnetic potentials. We impose a smallness condition on the…
This article is devoted to the study of local well-posedness for deep water waves with constant vorticity in two space dimensions on the real line. The water waves can be paralinearized and written as a quasilinear dispersive system of…
Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time…
A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind…
This is the second part of our work initiating the rigorous study of wave turbulence for water waves equations. We combine energy estimates, normal forms, and probabilistic and combinatorial arguments to complete the construction of…
An experimental validation of theoretical models of transmission of regular water waves by large arrays of floating disks is presented. The experiments are conducted in a wave basin. The models are based on combined potential-flow and…
In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a graph and ends in a splash. Numerical simulations lead to an…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We derive here a variant of the 2D Green-Naghdi equations that model the propagation of two-directional, nonlinear dispersive waves in shallow water. This new model has the same accuracy as the standard $2D $ Green-Naghdi equations. Its…
We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…
In this paper, we study the endpoint reversed Strichartz estimates along general time-like trajectories for wave equations in $\mathbb{R}^{3}$. We also discuss some applications of the reversed Strichartz estimates and the structure of wave…
This paper focuses on the analysis of stratified steady periodic water waves that contain stagnation points. The initial step involves transforming the free-boundary problem into a quasilinear pseudodifferential equation through a conformal…
The diffusive viscous wave equation describes wave propagation in diffusive and viscous media. Examples include seismic waves traveling through the Earth's crust, taking into account of both the elastic properties of rocks and the…
We consider the wave equation on a manifold $(\Omega,g)$ of dimension $d\geq 2$ with smooth strictly convex boundary $\partial\Omega\neq\emptyset$, with Dirichlet boundary conditions. We construct a sharp local in time parametrix and then…
We consider stratified steady water waves in a two dimensional channel. Our main subject is spectral properties of the Frechet derivatives of steady water Stokes waves. One of main results is the absence of subharmonic water waves in a…
The fractional wave equation governs the propagation of mechanical diffusive waves in viscoelastic media which exhibits a power-law creep, and consequently provided a physical interpretation of this equation in the framework of dynamic…
We study the stabilization and the wellposedness of solutions of the wave equation with subcritical semilinearities and locally distributed nonlinear dissipation. The novelty of this paper is that we deal with the difficulty that the main…
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…
We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…