Hydrodynamic limit of the Kuramoto-Sakaguchi equation with inertia and noise effects
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910637571964928 |
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| author | Mai, Tina |
| author_facet | Mai, Tina |
| contents | We consider the Kuramoto-Sakaguchi-Fokker-Planck equation (namely, parabolic Kuramoto-Sakaguchi, or Kuramoto-Sakaguchi equation, which is a nonlinear parabolic integro-differential equation) with inertia and white noise effects. We study the hydrodynamic limit of this Kuramoto-Sakaguchi equation. During showing this main result, as a support, we also prove a Hardy-type inequality over the whole real line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05113 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit of the Kuramoto-Sakaguchi equation with inertia and noise effects Mai, Tina Analysis of PDEs Mathematical Physics 92B25, 35Q84, 35Q70, 34C15, 35Q35 We consider the Kuramoto-Sakaguchi-Fokker-Planck equation (namely, parabolic Kuramoto-Sakaguchi, or Kuramoto-Sakaguchi equation, which is a nonlinear parabolic integro-differential equation) with inertia and white noise effects. We study the hydrodynamic limit of this Kuramoto-Sakaguchi equation. During showing this main result, as a support, we also prove a Hardy-type inequality over the whole real line. |
| title | Hydrodynamic limit of the Kuramoto-Sakaguchi equation with inertia and noise effects |
| topic | Analysis of PDEs Mathematical Physics 92B25, 35Q84, 35Q70, 34C15, 35Q35 |
| url | https://arxiv.org/abs/2410.05113 |