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arXiv · 2301.06659

Global solutions of stochastic nonlinear Schr\"odinger system with quadratic interaction

Masaru Hamano·Shunya Hashimoto·Shuji Machihara
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Abstract

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.

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Masaru Hamano, Shunya Hashimoto, Shuji Machihara. 2023-01-17. Global solutions of stochastic nonlinear Schr\"odinger system with quadratic interaction. https://arxiv.org/abs/2301.06659

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