Hypocoercive estimates on foliations and velocity spherical Brownian motion

TY - JOUR

T1 - Hypocoercive estimates on foliations and velocity spherical Brownian motion

AU - Baudoin, Fabrice

AU - Tardif, Camille

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2018

Y1 - 2018

N2 - By further developing the generalized Γ-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations. We study then in detail the example of the velocity spherical Brownian motion, whose generator is a step-3 generating hypoelliptic Hörmander's type operator. To prove hypocoercivity in that case, the key point is to show the existence of a convenient Riemannian foliation associated to the diffusion. We will then deduce, under suitable geometric conditions, the convergence to equilibrium of the diffusion in H1 and in L2.

AB - By further developing the generalized Γ-calculus for hypoelliptic operators, we prove hypocoercive estimates for a large class of Kolmogorov type operators which are defined on non necessarily totally geodesic Riemannian foliations. We study then in detail the example of the velocity spherical Brownian motion, whose generator is a step-3 generating hypoelliptic Hörmander's type operator. To prove hypocoercivity in that case, the key point is to show the existence of a convenient Riemannian foliation associated to the diffusion. We will then deduce, under suitable geometric conditions, the convergence to equilibrium of the diffusion in H1 and in L2.

KW - Hypocoercivity

KW - Hypoelliptic diffusion

KW - Kolmogorov diffusion

KW - Sasaki metric

UR - http://www.scopus.com/inward/record.url?scp=85050723678&partnerID=8YFLogxK

U2 - 10.3934/KRM.2018001

DO - 10.3934/KRM.2018001

M3 - Journal article

AN - SCOPUS:85050723678

SN - 1937-5093

VL - 11

SP - 1

EP - 23

JO - Kinetic and Related Models

JF - Kinetic and Related Models

IS - 1

ER -