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February  2009, 23(1&2): 521-540. doi: 10.3934/dcds.2009.23.521

Upper semi-continuity of stationary statistical properties of dissipative systems

Xiaoming Wang 1,

1. 

Department of Mathematics, Florida State University, Tallahassee, FL32306

Received  November 2007 Revised  April 2008 Published  September 2008

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.
Keywords: invariant measure, upper semi-continuity, Rayleigh-Bénard convection, Stationary statistical solution, dissipative system.
Mathematics Subject Classification: Primary: 37L40, 37L15; Secondary: 35Q35, 76D06, 76M45.
Citation: Xiaoming Wang. Upper semi-continuity of stationary statistical properties of dissipative systems. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 521-540. doi: 10.3934/dcds.2009.23.521
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