Stochastic curve shortening flow driven by a transport-type pure jump Lévy noise
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866916000874627072 |
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| author | Ge, Xiaotian Shang, Shijie Wu, Weina Zhai, Jianliang |
| author_facet | Ge, Xiaotian Shang, Shijie Wu, Weina Zhai, Jianliang |
| contents | We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump Lévy noise. To obtain the existence and uniqueness of strong solutions, we transform the equation into its equivalent Itô-type stochastic partial differential equation via a transport equation, and apply the monotone method with Lyapunov-type conditions. The obstacles to investigate the long-time behavior are the weak dissipativity and singularity inherent in the equation. To this end, we establish an improved regularity and prove that these solutions converge pathwise to zero at an exponential rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10609 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic curve shortening flow driven by a transport-type pure jump Lévy noise Ge, Xiaotian Shang, Shijie Wu, Weina Zhai, Jianliang Probability 60H15, 60G51 We study the existence and uniqueness, the regularity, and the long-time behavior of strong solutions to stochastic curve shortening flow driven by a transport-type pure jump Lévy noise. To obtain the existence and uniqueness of strong solutions, we transform the equation into its equivalent Itô-type stochastic partial differential equation via a transport equation, and apply the monotone method with Lyapunov-type conditions. The obstacles to investigate the long-time behavior are the weak dissipativity and singularity inherent in the equation. To this end, we establish an improved regularity and prove that these solutions converge pathwise to zero at an exponential rate. |
| title | Stochastic curve shortening flow driven by a transport-type pure jump Lévy noise |
| topic | Probability 60H15, 60G51 |
| url | https://arxiv.org/abs/2605.10609 |