As a model problem for the barotropic mode of the primitive equations of the oceans and
atmosphere, we consider the Euler system on a bounded convex planar domain Ω …

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 …

Abstract In 1983, Antontsev, Kazhikhov, and Monakhov published a proof of the existence
and uniqueness of solutions to the 3D Euler equations in which on certain inflow boundary …

A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D
inviscid primitive equations. Numerical schemes using the splitting-up method are proposed …

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 …

We establish the vanishing viscosity limit of the zero-mode of the linearized Primitive
Equations in a cube. Our method is based on the explicit construction and estimates of the …

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 …

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 …

The authors consider a simple transport equation in one-dimensional space and the
linearized shallow water equations in two-dimensional space, and describe and implement …

New avenues are explored for the numerical study of the two dimensional inviscid
hydrostatic primitive equations of the atmosphere with humidity and saturation, in presence …