具有陷俘效应的哈密顿量的定量相位混合
Quantitative phase mixing for Hamiltonians with trapping
AI总结：
本文证明了一般哈密顿量驱动的线性输运方程解生成的宏观物理量的定量衰减估计，粒子轨迹被困于含非退化椭圆驻点的紧致相空间区域，涵盖径向对称的1+2维与1+1维情形。
摘要：
我们证明了一般哈密顿量族驱动的线性输运方程解所生成的宏观物理量的定量衰减估计。相关粒子轨迹均被困在相空间的紧致区域内，并具有非退化椭圆驻点。该分析涵盖了由引力 Vlasov-Poisson 系统的径向对称紧支平衡态生成的一大类哈密顿量。在径向对称下，我们的分析涵盖了 1+2 维情形以及更困难的 1+1 维情形，其中所有粒子具有相同的角动量模值。后一种情形在等离子体物理和二维不可压缩流体流动中同样具有重要意义。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
