Upper semi-continuity of stationary statistical properties of dissipative systems

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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

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

Received November 2007 Revised April 2008 Published September 2008

Abstract
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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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