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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.04966 |
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| _version_ | 1866913493863628800 |
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| author | Chang, Shengchuang Liu, Shuangqian Yang, Tong |
| author_facet | Chang, Shengchuang Liu, Shuangqian Yang, Tong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime Chang, Shengchuang Liu, Shuangqian Yang, Tong Analysis of PDEs 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. |
| title | The spatially inhomogeneous Vlasov-Nordström-Fokker-Planck system in the intrinsic weak diffusion regime |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.04966 |