88 research outputs found
A squeezing property and its applications to a description of long time behaviour in the 3D viscous primitive equations
We consider the 3D viscous primitive equations with periodic boundary
conditions. These equations arise in the study of ocean dynamics and generate a
dynamical system in a Sobolev H^1 type space. Our main result establishes the
so-called squeezing property in the Ladyzhenskaya form for this system. As a
consequence of this property we prove (i) the finiteness of the fractal
dimension of the corresponding global attractor, (ii) the existence of finite
number of determining modes, and (iii) ergodicity of a related random kick
model. All these results provide a new information concerning long time
dynamics of oceanic motions.Comment: 22 pages, corrected version with added appendi
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