Abstract
We study linear inhomogeneous kinetic equations with an external confining potential and a collision operator admitting several local conservation laws (local density, momentum and energy). We classify all special macroscopic modes (stationary solutions and time-periodic solutions). We also prove the convergence of all solutions of the evolution equation to such nontrivial modes, with a quantitative exponential rate. This is the first hypocoercivity result with multiple special macroscopic modes with constructive estimates depending on the geometry of the potential.
| Original language | English |
|---|---|
| Pages (from-to) | 1597-1659 |
| Number of pages | 63 |
| Journal | Journal of the European Mathematical Society |
| Volume | 28 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 18 Feb 2026 |
Keywords
- Poincaré–Korn inequality
- Witten–Laplace operator
- classification of steady states
- collision invariant
- collision operator
- confinement potential
- conservation laws
- hypocoercivity
- hypoellipticity
- linear kinetic equations
- local conservation laws
- micro/macro decomposition
- partially harmonic potential
- special macroscopic modes
- spectral gap
- time-periodic solutions
- transport operator
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