The well-posedness of the stochastic nonlinear Schrödinger equations in $H^2(\mathbb{R}^d)$
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866912146844024832 |
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| author | Dôku, Isamu Hashimoto, Shunya Machihara, Shuji |
| author_facet | Dôku, Isamu Hashimoto, Shunya Machihara, Shuji |
| contents | The Cauchy problem for the stochastic nonlinear Schrödinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients are purely imaginary numbers. The main purpose of this paper is to construct classical solutions in $H^2(\mathbb{R}^d)$ for the problem. The techniques of Kato \cite{K87,K89} work well in overcoming this difficulty even for the stochastic equations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2205_03095 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The well-posedness of the stochastic nonlinear Schrödinger equations in $H^2(\mathbb{R}^d)$ Dôku, Isamu Hashimoto, Shunya Machihara, Shuji Analysis of PDEs Probability 60H15, 35B65, 35J10 The Cauchy problem for the stochastic nonlinear Schrödinger equation with multiplicative noise is considered where the nonlinear term is of power type and the noise coefficients are purely imaginary numbers. The main purpose of this paper is to construct classical solutions in $H^2(\mathbb{R}^d)$ for the problem. The techniques of Kato \cite{K87,K89} work well in overcoming this difficulty even for the stochastic equations. |
| title | The well-posedness of the stochastic nonlinear Schrödinger equations in $H^2(\mathbb{R}^d)$ |
| topic | Analysis of PDEs Probability 60H15, 35B65, 35J10 |
| url | https://arxiv.org/abs/2205.03095 |