This work is devoted to the structure of the time-discrete Green--Naghdi equations including
bathymetry. We use the projection structure of the equations to characterize homogeneous …

A new method, with the non-fully mixed coefficient (NFMC) considered, was put forward to
calculate the water environmental carrying capacity (WECC) for huge river-connected lakes …

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 recover the initial status of an evolution system governed by linearized shallow-water
wave equations in a 2-dimensional bounded domain by data assimilation technique, with …

In this article we consider the inviscid two-dimensional shallow water equations in a
rectangle. The flow occurs near a stationary solution in the so called supercritical regime …

A new set of boundary conditions has been derived by rigorous methods for the shallow
water equations in a limited domain. The aim of this article is to present these boundary …

In this article we study the boundary layers for the viscous Linearized Primitive Equations
(LPEs) when the viscosity is small. The LPEs are considered here in a cube. Besides the …

We continue our study of the inviscid shallow water equations (SWE) in a rectangle. In an
earlier work (Huang and Temam in Arch Ration Mech Anal 211 (3): 1027–1063, 2014) we …

This review article concerns multi-level methods for finite volume discretizations. They are
presented in the context of the non-viscous shallow water equations in space dimension one …