Stochastic Schrödinger-Korteweg de Vries systems driven by multiplicative noises
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916952386043904 |
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| author | Chen, Jie Gu, Fan Guo, Boling |
| author_facet | Chen, Jie Gu, Fan Guo, Boling |
| contents | In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in $H_x^1\times H_x^1$. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear terms with $b\in\left(0,1/2\right)$. Then, to overcome regularity problems, we introduce a series of approximation equations with localized nonlinear terms, which are also cutted-off in both the physical and the frequency space. By limitations, these approximation equations will help us get a priori estimate in the Bourgain space and finish the proof of the global well-posedness of the initial system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stochastic Schrödinger-Korteweg de Vries systems driven by multiplicative noises Chen, Jie Gu, Fan Guo, Boling Probability 60H15, 35Q53, 35Q55 In this paper, we consider the well-posedness of stochastic S-KdV driven by multiplicative noises in $H_x^1\times H_x^1$. To get the local well-posedness, we first develop the bilinear and trilinear Bourgain norm estimates of the nonlinear terms with $b\in\left(0,1/2\right)$. Then, to overcome regularity problems, we introduce a series of approximation equations with localized nonlinear terms, which are also cutted-off in both the physical and the frequency space. By limitations, these approximation equations will help us get a priori estimate in the Bourgain space and finish the proof of the global well-posedness of the initial system. |
| title | Stochastic Schrödinger-Korteweg de Vries systems driven by multiplicative noises |
| topic | Probability 60H15, 35Q53, 35Q55 |
| url | https://arxiv.org/abs/2402.04669 |