THE RELAXATION SPEED IN THE CASE THE FLOW SATISFIES EXPONENTIAL DECAY OF CORRELATIONS

Brice Franke (1) , Thi-Hien Nguyen (1)

1 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

We study the convergence speed in L 2-norm of the diffusion semi-group toward its equilibrium when the underlying flow satisfies decay of correlation. Our result is some extension of the main theorem given by Constantin, Kiselev, Ryzhik and Zlatoš in [3]. 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.

Domaines: Mathématiques [math]

Brice Franke, Thi-Hien Nguyen. THE RELAXATION SPEED IN THE CASE THE FLOW SATISFIES EXPONENTIAL DECAY OF CORRELATIONS. Proceedings of the American Mathematical Society, 2018, 146 (6), pp.2425-2434. ⟨10.1090/proc/13268⟩. ⟨hal-01271798⟩