Global Existence and Long-Time Asymptotics for Rotating Fluids in a 3D Layer

@article{Gallay2009GlobalEA,
  title={Global Existence and Long-Time Asymptotics for Rotating Fluids in a 3D Layer},
  author={Thierry Gallay and Violaine Roussier-Michon},
  journal={arXiv: Analysis of PDEs},
  year={2009}
}
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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

SHOWING 1-10 OF 32 REFERENCES
Global regularity of 3D rotating Navier-Stokes equations for resonant domains
Ekman layers of rotating fluids: The case of general initial data
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
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
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
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
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
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
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
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
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…
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