Hypocoercivity of linear kinetic equations via Harris's Theorem

José Cañizo (1) , Chuqi Cao (2) , Josephine Evans (2) , Havva Yoldaş (3)

1 UGR - Universidad de Granada = University of Granada
2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
3 Basque Center for Applied Mathematics

We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus (x, v) ∈ T d × R d or on the whole space (x, v) ∈ R d × R d with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively L 1 or weighted L 1 norms). The convergence rates are exponential when the equations are posed on the torus, or with a confining potential growing at least quadratically at infinity. Moreover, we give algebraic convergence rates when subquadratic potentials considered. We use a method from the theory of Markov processes known as Harris's Theorem.

Domaines: Equations aux dérivées partielles [math.AP]

José Cañizo, Chuqi Cao, Josephine Evans, Havva Yoldaş. Hypocoercivity of linear kinetic equations via Harris's Theorem. 2019. ⟨hal-02049210v1⟩