Exponential Mixing for Hamiltonian Shear Flow
Abstract
Abstract. We consider the advection equation on [Formula: see text] with a real-analytic and time-periodic velocity field that alternates between two Hamiltonian shears. Randomness is injected by alternating the vector field randomly in time between just two distinct shears. We provide a sufficient condition guaranteeing that these models possess a positive top Lyapunov exponent and demonstrate optimal exponential mixing. This framework is then applied to four distinct models, including the randomized-time Pierrehumbert model.
Fields of Study & Subjects
Markov Chains and Monte Carlo Methods
Stochastic processes and statistical mechanics
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- SIAM Journal on Mathematical Analysis
- Volume
- 58
- Issue
- 2
- Pages
- 1900–1936
- Publication date
- 13 April 2026
- Language
- EN