齐次 Landau 方程的整体适定性
偏微分方程分析
2014-01-07 v2 数学物理
math.MP
摘要
我们证明了动力学理论中齐次 Landau 方程的整体适定性及其向平衡态的指数衰减。初始分布仅假设为有界且在无穷远处衰减足够快。特别地，这涵盖了可能远离平衡态的不连续初始构型。尽管该方程缺乏比较原理，存在性证明仍依赖于障碍论证与抛物正则性理论。随后通过加权积分不等式获得了唯一性和向平衡态的衰减。尽管本文重点在于具有库仑势的空间齐次情形，但此处引入的方法可应用于非线性动力学理论的其他领域。
引用
@article{arxiv.1305.2257,
title = {Global well-posedness for the homogeneous Landau equation},
author = {Maria Gualdani and Nestor Guillen},
journal= {arXiv preprint arXiv:1305.2257},
year = {2014}
}
备注
This paper has been withdrawn due to a crucial computational error in Prop. 2.1. Under the correct bound, the assumptions for a key barrier argument (Lemma 2.4) are hard to verify and might not hold with the generality needed. As the authors feel the proposed method is still of some value, a new but partial result (under extra assumptions, including radial symmetry) will be posted soon