具极软势的朗道方程行进麦克斯韦分布的线性稳定性
Linear stability of traveling Maxwellians for Landau equation with very soft potentials
浏览论文内容
中文总结 AI 辅助
本文研究具极软势的朗道方程行进麦克斯韦分布的线性稳定性，证明其线性解微观部分逆多项式衰减、宏观部分有界不衰减，且其长时间动力学与两类对比情况存在差异。
中文摘要 AI 辅助
考虑库仑势下朗道方程在行进麦克斯韦分布附近的线性化问题，我们证明线性解的微观部分以逆多项式速率衰减，而宏观部分保持有界但通常不衰减。特别地，其长时间动力学与两类情况不同：一是具中等软势或硬势的朗道方程行进麦克斯韦分布附近的线性化，二是任意势下全局（非行进）麦克斯韦分布附近的线性化。
英文摘要
Consider the Landau equation with a Coulomb potential linearized around traveling Maxwellians. We prove that the microscopic part of the linear solution decays with an inverse polynomial rate, while the macroscopic part remains bounded but in general does not decay. In particular, the long-time dynamics are different from the linearization around either (1) traveling Maxwellians for moderately soft or hard potentials or (2) global (non-traveling) Maxwellians (for any potentials).
