| 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 for the spatially inhomogeneous counterpart.
In this talk, we demonstrate that the Cauchy problem for the spatially inhomogeneous Vlasov-Nordstr\{o}m-Fokker-Planck system, without friction, maintains dynamic stability 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 within the framework of self-similar solutions. |
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