Stochastic Schr\'{o}dinger-Korteweg de Vries systems driven by multiplicative noises
| Autor: | Chen, Jie, Gu, Fan, Guo, Boling |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 the lack of the maximum functional estimate, we introduce a series of approximation equations with localized nonlinear terms, which are also cutted-off in both the physical and the Fourier 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. Comment: 41 pages |
| Databáze: | arXiv |
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