In this article we consider the Primitive Equations without horizontal viscosity but with a mild vertical viscosity added in the hydro-static equation, as in  and , which are the so-called δ−Primitive Equations. We prove that the problem is well posed in the sense of Hadamard in certain types of spaces. This means that we prove the finite-in-time… (More)
The aim of this paper is to study the well-posedness and long time behavior, in terms of finite-dimensional attractors, of a perturbed Cahn–Hilliard equation. This equation differs from the usual Cahn–Hilliard by the presence of the term ε(−Δu + f (u)). In particular, we prove the existence of a robust family of exponential attractors as ε goes to zero.
In this article we consider a system of equations related to the ␦-primitive equations of the ocean and the atmosphere, linearized around a stratified flow, and we supplement the equations with transparent boundary conditions. We study the stability of different numerical schemes and we show that for each case, letting the vertical viscosity ␦ go to 0, the… (More)