Quantitative phase mixing for Hamiltonians with trapping
Abstract
We prove quantitative decay estimates of macroscopic quantities generated by the solutions to linear transport equations driven by a general family of Hamiltonians. The associated particle trajectories are all trapped in a compact region of phase-space and feature a non-degenerate elliptic stagnation point. The analysis covers a large class of Hamiltonians generated by the radially symmetric compactly supported equilibria of the gravitational Vlasov-Poisson system. Working in radial symmetry, our analysis features both the 1+2-dimensional case and the harder 1+1-dimensional case, where all the particles have the same value of the modulus of angular momentum. The latter case is also of importance in both the plasma physics case and two dimensional incompressible fluid flows.
Cite
@article{arxiv.2405.17153,
title = {Quantitative phase mixing for Hamiltonians with trapping},
author = {Mahir Hadžić and Gerhard Rein and Matthew Schrecker and Christopher Straub},
journal= {arXiv preprint arXiv:2405.17153},
year = {2024}
}
Comments
60 pages, added the decay of the macroscopic density to Theorem 1.7