We consider the linearized 2D inviscid shallow water equations in a rectangle. A set of
boundary conditions is proposed which make these equations well-posed. Several different …

We investigate an initial-boundary value problem for the one-dimensional rotating shallow
water magnetohydrodynamic equations. The Dirichlet boundary conditions are imposed …

We consider the shallow water equations in the supercritical and subcritical cases in one
space variable, posed in a finite spatial interval with characteristic boundary conditions at …

In this article, we give an asymptotic expansion, with respect to the viscosity which is
considered here to be small, of the solutions of the 3D linearized Primitive Equations (EPs) …

The aim of this article is to study a model of two superposed layers of fluid governed by the
shallow water equations in space dimension one. Under some suitable hypotheses the …

The article is devoted to prove the existence and regularity of the solutions of the 3 D inviscid
Linearized Primitive Equations (LPEs) in a channel with lateral periodicity. This was …

This paper is concerned with an initial-boundary value problem for the two-dimensional
axisymmetric rotating shallow water equations. The Dirichlet boundary conditions are …

The numerical simulation of wave-like phenomena occurring in large or infinite domains is a
great challenge for a wide range of technological and scientifical problems. A classical way …

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 …

In this chapter, we describe numerical multilevel methods applied to the Navier–Stokes
equations (homogeneous isotropic turbulence and channel flow problem), to the shallow …