相关论文: Well-posedness of a water wave model with viscous …

In this paper, we address the question of the hyperbolicity and the local well- posedness of the multi-layer shallow water model, with free surface, in two dimensions. We first provide a general criterion that proves the symmetrizability of…

Consider a viscous fluid of finite depth below the air. In the absence of the surface tension effect at the air-fluid interface, the long time behavior of a free surface with small amplitude has been an intriguing question since the work of…

The hard phase model describes a relativistic barotropic and irrotational fluid with sound speed equal to the speed of light. In the framework of general relativity, the fluid, as a matter field, affects the geometry of the background…

Two-dimensional nonlinear gravity waves travelling in shallow water on a vertically sheared current of constant vorticity are considered. Using Euler equations, in the shallow water approximation, hyperbolic equations for the surface…

We consider the gravity-capillary water waves problem in a domain $\Omega_t \subset \mathbb{T} \times \mathbb{R}$ with substantial geometric features. Namely, we consider a variable bottom, smooth obstacles in the flow and a constant…

We study the motion of a compressible perfect liquid body in vacuum. This can be thought of as a model for the motion of the ocean or a star. The free surface moves with the velocity of the liquid and the pressure vanishes on the free…

We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…

The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…

This work focuses on the mathematical analysis of the Cauchy problem associated with a two-dimensional equation describing the dynamics of a thin fluid film flowing down an inclined flat plate under the influence of gravity and an electric…

By performing two parallel numerical experiments -- solving the dynamical Hamiltonian equations and solving the Hasselmann kinetic equation -- we examined the applicability of the theory of weak turbulence to the description of the time…

We consider higher order viscous Burgers' equations with generalized nonlinearity and study the associated initial value problems for given data in the $L^2$-based Sobolev spaces. We introduce appropriate time weighted spaces to derive…

In the framework of general relativity, the dynamics of a general barotropic fluid are coupled to the Einstein equations, which govern the structure of the underlying spacetime. We establish a priori estimates and well-posedness in Sobolev…

In this paper we apply the approach of formal asymptotic expansions and perturbation theory to derive a new highly nonlinear shallow-water model from the full governing equations for two dimensional incompressible fluid with constant…

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq…

In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume…

In this paper, we consider a free boundary problem of the incompressible elatodynamics, a coupling system of the Euler equations for the fluid motion with a transport equation for the deformation tensor. Under a natural force balance law on…

We consider in this article the system of (pure) gravity water waves in any dimension and in fluid domains with general bottoms. The unique solvability of the problem was established by Alazard-Burq-Zuily [Invent. Math, 198 (2014), no. 1,…

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 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…