Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case

2019/02/10 by Deng Zhang, Zhang, Deng · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.03559

openalex publication_date 2019/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study optimal bilinear control problems for stochastic nonlinear Schrödinger equations in both the mass subcritical and critical case. For general initial data of the minimal L2 regularity, we prove the existence and first order Lagrange condition of an open loop control. Furthermore, we obtain uniform estimates of (backward) stochastic solutions in new spaces of type U2 and V2, adapted to evolution operators related to linear Schrödinger equations with lower order perturbations. In particular, we obtain a new temporal regularity of rescaled (backward) stochastic solutions, which is the key ingredient in the proof of tightness of approximating controls induced by Ekeland's variational principle.

Cited by

• Optimality Conditions for Control Systems Governed by Monotone Stochastic Evolution Equations
• Multi-solitons to focusing mass-supercritical stochastic nonlinear Schrödinger equations

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