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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2503.00343 |
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| _version_ | 1866909518053507072 |
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| author | Yamazaki, Kazuo |
| author_facet | Yamazaki, Kazuo |
| contents | We consider the one-dimensional Burgers' equation forced by fractional derivative of order $\frac{1}{2}$ applied on space-time white noise. Relying on the approaches of Anderson Hamiltonian from Allez and Chouk (2015, arXiv:1511.02718 [math.PR]) and two-dimensional Navier-Stokes equations forced by space-time white noise from Hairer and Rosati (2024, Annals of PDE, \textbf{10}, pp. 1--46), we prove the global-in-time existence and uniqueness of its mild and weak solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00343 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise Yamazaki, Kazuo Analysis of PDEs Probability We consider the one-dimensional Burgers' equation forced by fractional derivative of order $\frac{1}{2}$ applied on space-time white noise. Relying on the approaches of Anderson Hamiltonian from Allez and Chouk (2015, arXiv:1511.02718 [math.PR]) and two-dimensional Navier-Stokes equations forced by space-time white noise from Hairer and Rosati (2024, Annals of PDE, \textbf{10}, pp. 1--46), we prove the global-in-time existence and uniqueness of its mild and weak solutions. |
| title | Global unique solution to the perturbation of the Burgers' equation forced by derivatives of space-time white noise |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2503.00343 |