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The speed of relaxation for diffusion with drift satisfying exponential decay of correlations


Authors: Brice Franke and Thi-Hien Nguyen
Journal: Proc. Amer. Math. Soc. 146 (2018), 2425-2434
MSC (2010): Primary 35K10; Secondary 37A25, 60J60
DOI: https://doi.org/10.1090/proc/13268
Published electronically: February 28, 2018
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Abstract: We study the convergence speed in the $ L^2$-norm of the diffusion semigroup toward its equilibrium when the underlying flow satisfies decay of correlation. Our result is an extension of the main theorem given by Constantin, Kiselev, Ryzhik and Zlatoš (2008). Our proof is based on Weyl asymptotic law for the eigenvalues of the Laplace operator, Sobolev imbedding and some assumption on decay of correlation for the underlying flow.


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Additional Information

Brice Franke
Affiliation: Laboratiore de Mathématiques de Bretagne Atlantique UMR 6205, UFR Sciences et Techniques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, CS 93837, 29238 Brest, cedex 3, France
Email: brice.franke@univ-brest.fr

Thi-Hien Nguyen
Affiliation: Laboratiore de Mathématiques de Bretagne Atlantique UMR 6205, UFR Sciences et Techniques, Université de Bretagne Occidentale, 6 Avenue Le Gorgeu, CS 93837, 29238 Brest, cedex 3, France
Email: thi-hien.nguyen@univ-brest.fr

DOI: https://doi.org/10.1090/proc/13268
Keywords: Decay of correlation, relaxation speed, enhancement of diffusivity, non-self-adjoint generator, incompressible drift
Received by editor(s): May 22, 2015
Received by editor(s) in revised form: April 27, 2016
Published electronically: February 28, 2018
Additional Notes: The authors would like to thank their colleague Benoît Saussol for directing their attention to the notion of decay of correlation and Sheu Shuenn-Jyi for some helpful comments during a talk at National Central Taiwan University.
Communicated by: Joachim Krieger
Article copyright: © Copyright 2018 American Mathematical Society

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