Well-posedness of the Stochastic Degasperis-Procesi Equation
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910589008216064 |
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| author | Arruda, Lynnyngs K. Chemetov, Nikolai V. Cipriano, Fernanda |
| author_facet | Arruda, Lynnyngs K. Chemetov, Nikolai V. Cipriano, Fernanda |
| contents | This article studies the Stochastic Degasperis-Procesi (SDP) equation on $\mathbb{R}$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $L^2(\mathbb{R})\cap L^{2+δ}(\mathbb{R})$, for arbitrary small $δ>0$, we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00548 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Well-posedness of the Stochastic Degasperis-Procesi Equation Arruda, Lynnyngs K. Chemetov, Nikolai V. Cipriano, Fernanda Probability Analysis of PDEs 35R60, 60H15 This article studies the Stochastic Degasperis-Procesi (SDP) equation on $\mathbb{R}$ with an additive noise. Applying the kinetic theory, and considering the initial conditions in $L^2(\mathbb{R})\cap L^{2+δ}(\mathbb{R})$, for arbitrary small $δ>0$, we establish the existence of a global pathwise solution. Restricting to the particular case of zero noise, our result improves the deterministic solvability results that exist in the literature. |
| title | Well-posedness of the Stochastic Degasperis-Procesi Equation |
| topic | Probability Analysis of PDEs 35R60, 60H15 |
| url | https://arxiv.org/abs/2409.00548 |