Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up

2023/08/20 by Zhang, Ao, Zhang, Yanjie, Duan, Jinqiao
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.10270

Abstract

This work investigates radial solutions for nonlinear fractional Schrödinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz estimates, we establish local well-posedness in the energy-subcritical regime for the stochastic fractional nonlinear Schrödinger equation. Global existence is subsequently demonstrated through stochastic evolution of mass and energy. In focusing supercritical settings, we derive blow-up criteria via localized virial inequality, revealing how multiplicative noise measurably suppresses blow-up formation compared to deterministic dynamics.

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