Global solutions of stochastic nonlinear Schr\"odinger system with quadratic interaction
The time-global existence of solutions to a system of stochastic Schr\"odinger equations with multiplicative noise and the quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in [18] where the mass and energy are conserved. In our st...
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| Zusammenfassung: | The time-global existence of solutions to a system of stochastic
Schr\"odinger equations with multiplicative noise and the quadratic nonlinear
terms are discussed in this paper. The same system in the deterministic
treatment was studied in [18] where the mass and energy are conserved. In our
stochastic situation, those are not conserved and which causes several
difficulties in the arguments of composing a-priori estimate. |
|---|---|
| DOI: | 10.48550/arxiv.2301.06659 |