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arXiv · 2409.04966

The spatially inhomogeneous Vlasov-Nordstr\"{o}m-Fokker-Planck system in the intrinsic weak diffusion regime

Shengchuang Chang·Shuangqian Liu·Tong Yang
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Abstract

The spatially homogeneous Vlasov-Nordstr\"{o}m-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-Nordstr\"{o}m-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.

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Shengchuang Chang, Shuangqian Liu, Tong Yang. 2024-09-08. The spatially inhomogeneous Vlasov-Nordstr\"{o}m-Fokker-Planck system in the intrinsic weak diffusion regime. https://arxiv.org/abs/2409.04966

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