2018/01/19 by Ruiwen Shu, Shi Jin, Shu, Ruiwen +1 · 1 citation
Decision Sciences · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems #Probabilistic and Robust Engineering Design #math.AP
paper · pdf · doi:10.48550/arxiv.1801.06304
arxiv created 2018/01/19 · openalex publication_date 2018/01/19 · arxiv updated 2018/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For the Vlasov-Poisson equation with random uncertain initial data, we prove that the Landau damping solution given by the deterministic counterpart (Caglioti and Maffei, \it J. Stat. Phys., 92:301-323, 1998) depends smoothly on the random variable if the time asymptotic profile does, under the smoothness and smallness assumptions similar to the deterministic case. The main idea is to generalize the deterministic contraction argument to more complicated function spaces to estimate derivatives in space, velocity and random variables. This result suggests that the random space regularity can persist in long-time even in time-reversible nonlinear kinetic equations.