Upper semi-continuity of stationary statistical properties of dissipative systems

Xiaoming Wang

doi:10.3934/dcds.2009.23.521

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2009, Volume 23, Issue 1&2: 521-540. Doi: 10.3934/dcds.2009.23.521

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Upper semi-continuity of stationary statistical properties of dissipative systems

Xiaoming Wang^1,

1.
Department of Mathematics, Florida State University, Tallahassee, FL32306

Received: October 31, 2007

Revised: March 31, 2008

Published: April 2009

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Abstract

We show that stationary statistical properties for uniformlydissipative dynamical systems are upper semi-continuous underregular perturbation and a special type of singular perturbationin time of relaxation type. The results presented are applicableto many physical systems such as the singular limit of infinitePrandtl-Darcy number in the Darcy-Boussinesq system forconvection in porous media, or the large Prandtl asymptotics forthe Boussinesq system.

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Mathematics Subject Classification: Primary: 37L40, 37L15; Secondary: 35Q35, 76D06, 76M45.

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