تقرير
Quantitative phase mixing for Hamiltonians with trapping
| العنوان: | Quantitative phase mixing for Hamiltonians with trapping |
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| المؤلفون: | Hadžić, Mahir, Rein, Gerhard, Schrecker, Matthew, Straub, Christopher |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Analysis of PDEs, Mathematical Physics, Mathematics - Dynamical Systems |
| الوصف: | 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. Comment: 60 pages, added the decay of the macroscopic density to Theorem 1.7 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.17153 |
| رقم الأكسشن: | edsarx.2405.17153 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |