2024/09/08 by Shengchuang Chang, Chang, Shengchuang, Shuangqian Liu +3
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #Statistical Mechanics and Entropy #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2409.04966
openalex publication_date 2024/09/08 · openalex created_date 2024/10/22 · openalex updated_date 2026/07/28
The spatially homogeneous Vlasov-Nordström-Fokker-Planck system is known to exhibit nontrivial large time behavior, naturally leading to weak diffusion of the Fokker-Planck operator. This weak diffusion, combined with the singularity of relativistic velocity, present a significant challenge in analysis for the spatially inhomogeneous counterpart. In this paper, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system, without friction, maintains dynamically stable relative to the corresponding spatially homogeneous system. Our results are twofold: (1) we establish the existence of a unique global classical solution and characterize the asymptotic behavior of the spatially inhomogeneous system using a refined weighted energy method; (2) we directly verify the dynamic stability of the spatially inhomogeneous system in the framework of self-similar solutions.