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

DOI10.1007/s00440-020-00971-0zbMath1447.60127arXiv1902.03559OpenAlexW3015782749MaRDI QIDQ2200493

Deng Zhang

Publication date: 22 September 2020

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1902.03559

zbMATH Keywords

optimal controlWiener processnonlinear Schrödinger equationbackward stochastic equation\(U^p-V^p\) spaces

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) PDEs in connection with quantum mechanics (35Q40) Schrödinger operator, Schrödinger equation (35J10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Optimality conditions for problems involving randomness (49K45)

Related Items (8)

Strichartz and Local Smoothing Estimates for Stochastic Dispersive Equations with Linear Multiplicative Noise ⋮ Multi solitary waves to stochastic nonlinear Schrödinger equations ⋮ Multi-bubble Bourgain-Wang solutions to nonlinear Schrödinger equations ⋮ Stochastic nonlinear Schrödinger equations in the defocusing mass and energy critical cases ⋮ Optimal Control of Nonlinear Stochastic Differential Equations on Hilbert Spaces ⋮ Construction of minimal mass blow-up solutions to rough nonlinear Schrödinger equations ⋮ On uniqueness of multi-bubble blow-up solutions and multi-solitons to \(L^2\)-critical nonlinear Schrödinger equations ⋮ Global well-posedness for the defocussing mass-critical stochastic nonlinear Schrödinger equation on \(\mathbb{R}\) at \(L^2\) regularity

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