Wednesday, July 15, 2020 - 14:00 in ZOOM - Video Conference
Optimal bilinear control of stochastic nonlinear Schrödinger equations: mass-(sub)critical case
A talk in the Bielefeld Stochastic Afternoon series by
Deng Zhang from Shanghai Jiao Tong University
| Abstract: |
Please contact stochana@math.uni-bielefeld.de for Meeting-ID and Password.
In this talk we consider the optimal control problems for stochastic nonlinear Schrödinger equations in both the mass subcritical and critical case. For general initial data of the minimal $L^2$ regularity, we prove the existence and first order Lagrange condition of an open loop control. In particular, these results apply to the stochastic nonlinear Schrödinger equations with the critical quintic and cubic nonlinearities in dimensions one and two, respectively.
Furthermore, we obtain uniform estimates of (backward) stochastic solutions in new spaces of type $U^2$ and $V^2$, adapted to the evolution operators related to linear Schrödinger equations with lower order perturbations, which yield a new temporal regularity of (backward) stochastic solutions.
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