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January & 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 uniformly dissipative dynamical systems are upper semi-continuous under regular perturbation and a special type of singular perturbation in time of relaxation type. The results presented are applicable to many physical systems such as the singular limit of infinite Prandtl-Darcy number in the Darcy-Boussinesq system for convection in porous media, or the large Prandtl asymptotics for the 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 & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 521-540. doi: 10.3934/dcds.2009.23.521
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