This chapter is devoted to the study of some asymptotic problems in hydrodynamics. In
particular, we will review results about the inviscid limit, the compressible–incompressible …

Primitive Equations (PEs) for the large scale ocean under the small depth hypothesis. The
small depth hypothesis implies that the domain Mε occupied by the ocean is a thin domain …

We consider the Navier-Stokes equations on a thin domain of the form Ωε= x∈ ℝ3| x1,
x2∈(0, 1), 0< x3< εg (x1, x2) supplemented with the following mixed boundary conditions …

This article is concerned with the study of the initial value problem for the three-dimensional
viscous Boussinesq system in the thin domain Ω≔ R 2×(0, R). We construct a global finite …

The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and
harmonic confining potential is considered. More precisely, the confining potential is strongly …

In this article we consider weak solutions of the three-dimensional incompressible fluid flow
equations with initial data admitting a one-dimensional symmetry group. We examine both …

We show that for a certain family of initial data, there exist non-unique weak solutions to the
3D incompressible Euler equations satisfying the weak energy inequality, whereas the weak …

Our Earth's atmosphere and oceans are rotating geophysical fluids that are two important
components of the planet's climate system. The atmosphere and the oceans are extremely …

Abstract We consider the Navier–Stokes equations in the thin 3D domain T _2 * (0, ϵ),
where T _2 is a two-dimensional torus. The equation is perturbed by a non-degenerate …

In this article we study the asymptotic behavior of solutions of the primitive equations (PEs)
as the depth of the domain goes to zero. We prove that the solutions of the PEs can be …