2017/04/01 by Shi Jin, Jin, Shi, Yuhua Zhu +1 · 2 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.1704.00208
openalex publication_date 2017/04/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/08/01
We study the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field or parabolic regimes. With the help of proper Lyapunov-type inequalities, under some mild conditions on the initial data, the regularity of the solution in the random space, as well as exponential decay of the solution to the global Maxwellian, are established under Sobolev norms, which are \it uniform in terms of the scaling parameters. These are the first hypocoercivity results for a nonlinear kinetic system with random input, which are important for the understanding of the sensitivity of the system under random perturbations, and for the establishment of spectral convergence of popular numerical methods for uncertainty quantification based on (spectrally accurate) polynomial chaos expansions.