相关论文: Quasi-planar steep water waves

Physics of nonlinear waves on variable backgrounds and the relevant mathematical analysis continues to be the challenging aspect of the study. In this work, we consider a (3+1)-dimensional nonlinear model describing the dynamics of {water…

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…

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…

We consider maps between Riemannian manifolds in which the map is a stationary point of the nonlinear Hodge energy. The variational equations of this functional form a quasilinear, nondiagonal, nonuniformly elliptic system which models…

We provide analytic solutions of the nonlinear differential equation system describing the particle paths below small-amplitude periodic gravity waves travelling on a constant vorticity current. We show that these paths are not closed…

Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…

This article provides a survey on some main results and recent developments in the mathematical theory of water waves. More precisely, we briefly discuss the mathematical modeling of water waves and then we give an overview of local and…

The paper continues to study the long-standing problem of quasi 1-D (one dimensional) spectrum of sea surface wave turbulence. The study is based on Hasselmann's kinetic equation, which significantly simplifies for the quasi 1-D turbulence.…

A Hamiltonian model for the propagation of internal water waves interacting with surface waves, a current and an uneven bottom is examined. Using the so-called Dirichlet-Neumann operators, the water wave system is expressed in the…

In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by…

We present a numerical study of spatially quasi-periodic traveling waves on the surface of an ideal fluid of infinite depth. This is a generalization of the classic Wilton ripple problem to the case when the ratio of wave numbers satisfying…

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…

Process of the nonlinear deformation of the shallow water wave in a basin of constant depth is studied. The characteristics of the first breaking are analyzed in details. The Fourier spectrum and steepness of the nonlinear wave is…

At its core, hydrodynamics is a many-body low-energy effective theory for the long-wavelength, long-timescale dynamics of conserved charges in systems close to thermodynamic equilibrium. It has a wide range of applications spanning from…

The quasi-streamfunction (Psi) formalism proposed by Kim et. al. (J.W. Kim, K.J. Bai, R.C. Ertekin, W.C. Webster, J. Eng. Math. 40, 17 (2001)) provides a natural framework for systematically studying zero-vorticity waves over arbitrary…

We study the Cauchy problem for a quasilinear wave equation with low-regularity data. A space-time $L^2$ estimate for the variable coefficient wave equation plays a central role for this purpose. Assuming radial symmetry, we establish the…

For the short pulse initial data with a first order outgoing constraint condition and optimal orders of smallness, we establish the global existence of smooth solutions to 2D quasilinear wave equations with higher order null conditions.…

In this work we prove the equivalence between three different weak formulations of the steady periodic water wave problem where the vorticity is discontinuous. In particular, we prove that generalised versions of the standard Euler and…

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…

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…