Related papers: Strichartz Estimates for Water Waves
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for…
Frequently encountered in nature, internal solitary waves in stratified fluids are well-observed and well-studied from the experimental, the theoretical, and the numerical perspective. From the mathematical point of view, these waves are…
In this paper, we mainly consider two class of travelling stratified periodic water waves, one with negative (or without) surface tension and the other with constant Bernoulli's function and stagnation points. We first establish the…
In this paper, I will summarize the uniform decay estimates of the discrete wave equations (DW) established by the oscillatory integral theory in [Sch98, BCH23, BCH24], and combine the abstract framework of the scattering theory of the…
We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields…
We modify the nonlinear shallow water equations, the Korteweg-de Vries equation, and the Whitham equation, to permit constant vorticity, and examine wave breaking, or the lack thereof. By wave breaking, we mean that the solution remains…
We study the instability of standing waves for nonlinear Schr\"{o}dinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimension. For that purpose, we establish a…
A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…
In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations. Small amplitude waves are studied within the linearization approximation…
This paper investigates the critical quintic wave equation in a 3D bounded domain subject to locally distributed Kelvin-Voigt damping. The study tackles two major mathematical challenges: the severe loss of derivatives induced by the…
In this paper, we embark on a captivating exploration of the stabilization of locally transmitted problems within the realm of two interconnected wave systems. To begin, we wield the formidable Arendt-Batty criteria\cite{AW} to affirm the…
We prove the (local in time) Strichartz estimates (for the full range of parameters given by the scaling unless the end point) for asymptotically flat and non trapping perturbations of the flat Laplacian in $\R^n$, $n\geq 2$. The main point…
The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…
Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
We investigate second order linear wave equations in periodic media, aiming at the derivation of effective equations in $\R^n$, $n \in \{1, 2, 3\}$. Standard homogenization theory provides, for the limit of a small periodicity length…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
A standard bilinear $L^2$ Strichartz estimate for the wave equation, which underlies the theory of $X^{s,b}$ spaces of Bourgain and Klainerman-Machedon, asserts (roughly speaking) that if two finite-energy solutions to the wave equation are…
A general method for calculating statistical properties of speckle patterns of coherent waves propagating in disordered media is developed. It allows one to calculate speckle pattern correlations in space, as well as their sensitivity to…