Abstract
We analyze time averages of the norm of solutions to kinetic Fokker-Planck equations related to general Hamiltonians. We present detailed and constructive decay estimates for systems influenced by a confining potential, which accommodates fat-tail, subexponential, and (super-)exponential local equilibria, including the traditional Maxwellian scenario. A crucial component of our estimates is a modified Poincaré inequality, derived using a Lions-Poincaré inequality and an averaging lemma.
| Original language | English |
|---|---|
| Pages (from-to) | 3587-3622 |
| Number of pages | 36 |
| Journal | SIAM Journal on Mathematical Analysis |
| Volume | 57 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 1 Jan 2025 |
Keywords
- Fokker-Planck equations
- Langevin dynamics
- Poincaré-Lions inequality
- exponential and algebraic convergence rates
- hypocoercivity