## 3 Citations

Asymptotic limit of fast rotation for the incompressible Navier–Stokes equations in a 3D layer

- Mathematics
- 2021

We consider the initial value problem for the Navier–Stokes equation with the Coriolis force in a three-dimensional infinite layer. We prove the unique existence of global solutions for initial data…

Vortices in stably-stratified rapidly rotating Boussinesq convection

- Physics, Environmental ScienceNonlinearity
- 2019

We study the Boussinesq approximation for rapidly rotating stably-stratified fluids in a three dimensional infinite layer with either stress-free or periodic boundary conditions in the vertical…

Global Axisymmetric Euler Flows with Rotation

- Mathematics
- 2021

We construct a class of global, dynamical solutions to the 3d Euler equations near the stationary state given by uniform “rigid body” rotation. These solutions are axisymmetric, of Sobolev…

## References

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- MathematicsAppl. Math. Lett.
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Ekman layers of rotating fluids: The case of general initial data

- Mathematics
- 2000

In this paper we describe the weak solutions of the Navier-Stokes equations with a large Coriolis term as the Rossby and the Ekman numbers go to zero in a special domain with various boundary…

Navier-Stokes Equations in Thin 3D Domains III: Existence of a Global Attractor

- Mathematics
- 1993

Over 50 years ago, Leray (1933, 1934a, 1934b) published his pioneering works on the Navier-Stokes equations which led to the modern mathematical theory of fluid dynamics. These equations describe the…

Ekman layers of rotating fluids, the case of well prepared initial data

- Mathematics
- 1997

In this paper we study the convergence of weak solutions of the Navier Stokes equations with a large Coriolis term as the Rossby and Ekman numbers go to zero, and in particular the so called Ekman…

Global Stability of Vortex Solutions of the Two-Dimensional Navier-Stokes Equation

- Physics, Mathematics
- 2005

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing…

On the Navier-Stokes initial value problem. I

- Mathematics
- 1964

Abstract : The initial value problem for the nonstationary Navier-Stokes equation is considered. New results were obtained with the aid of various methods from modern functional analysis. The…

Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2

- Mathematics
- 2001

Abstract We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R2 and show that these manifolds control the long-time behavior of the solutions. This…

Necessary and sufficient conditions of global nonlinear stability for rotating double-diffusive convection in a porous medium

- Mathematics
- 2002

The nonlinear stability of the conduction-diffusion solution of a fluid mixture heated and salted from below (and of a homogeneous fluid heated from below) and saturating a porous medium is studied…

Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag

- Mathematics
- 1988

Contents: General results and concepts on invariant sets and attractors.- Elements of functional analysis.- Attractors of the dissipative evolution equation of the first order in time:…

The Energy Method, Stability, and Nonlinear Convection

- Physics
- 1991

Introduction*Illustration of the energy method*The Navier-Stokes equations and the Benard problem*Symmetry, Competing Effects, and Coupling Parameters*Convection problems in a half space*Generalized…