Stochastic nonlinear Schrödinger equations on tori
| Autor: | Kelvin Cheung, Razvan Mosincat |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Statistics and Probability
Physics Partial differential equation Applied Mathematics Numerical analysis 010102 general mathematics Multiplicative function Mathematics::Analysis of PDEs Space (mathematics) 01 natural sciences Schrödinger equation Quintic function 010101 applied mathematics Sobolev space Nonlinear system symbols.namesake Modeling and Simulation symbols 0101 mathematics Nonlinear Sciences::Pattern Formation and Solitons Mathematical physics |
| Zdroj: | Cheung, K & Mosincat, R 2019, ' Stochastic nonlinear Schrödinger equations on tori ', Stochastics and Partial Differential Equations: Analysis and Computations, vol. 7, no. 2, pp. 169-208 . https://doi.org/10.1007/s40072-018-0125-x |
| ISSN: | 2194-041X 2194-0401 |
| DOI: | 10.1007/s40072-018-0125-x |
| Popis: | We consider the stochastic nonlinear Schrodinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in $$L^2(\mathbb {T})$$ . As for other power-type nonlinearities, namely (i) (super)quintic when $$d = 1$$ and (ii) (super)cubic when $$d \ge 2$$ , we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems. |
| Databáze: | OpenAIRE |
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