Small-time approximate controllability of the logarithmic Schrödinger equation
Abstract
We consider Schrödinger equations with logarithmic nonlinearity and bilinear controls, posed on T d or ℝ d . We prove their small-time global L 2 -approximate controllability. The proof consists in extending to this nonlinear framework the approach introduced by the first and third authors in [K. Beauchard and E. Pozzoli, Ann. Inst. H. Poincaré Anal. Non Linéaire (2025)] to control the linear equation: it combines the small-time controllability of phases and gradient flows. Due to the nonlinearity, the required estimates are more difficult to establish than in the linear case. The proof here is inspired by WKB analysis. This is the first result of (small-time) global approximate controllability, for nonlinear Schrodinger equations, with bilinear controls.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Stability and Controllability of Differential Equations
Numerical methods for differential equations
Publication details
- Journal / source
- ESAIM Control Optimisation and Calculus of Variations
- Publisher
- EDP Sciences
- Volume
- 32
- Pages
- 46–46
- Publication date
- 1 January 2026
- Language
- EN