A squeezing property and its applications to a description of long-time behaviour in the three-dimensional viscous primitive equations. Issue 4 (24th July 2014)

• Record Type: Journal Article
• Authors: Chueshov, Igor
• Is Part Of: Proceedings. Volume 144:Issue 4(2014)
• Page Start: 711
• Page End: 729
• Publication Date: 2014-07-24
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210512001953
• Languages: English
• ISSNs: 0308-2105

Abstract

<abstract abstract-type="normal"> <title> <x content-type="archive" xml:space="preserve">Abstract</x> </title> <p>We consider the three-dimensional viscous primitive equations with periodic boundary conditions. These equations arise in the study of ocean dynamics and generate a dynamical system in a Sobolev <italic>H</italic>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 the finiteness of the fractal dimension of the corresponding global attractor, the existence of a finite number of determining modes and the ergodicity of a related random kick model. All these results provide new information concerning the long-time dynamics of oceanic motion.</p> </abstract>