Carleman estimates for forward and backward stochastic fourth order Schr\"odinger equations and their applications

TL;DR

This paper develops Carleman estimates for stochastic fourth order Schrödinger equations, enabling results on observability, unique continuation, and controllability for these complex stochastic PDEs.

Contribution

It introduces novel Carleman estimates for both forward and backward stochastic fourth order Schrödinger equations, advancing control theory in stochastic PDEs.

Findings

Established Carleman estimates for stochastic fourth order Schrödinger equations

Proved observability and unique continuation properties

Achieved exact controllability results for the equations

Abstract

In this paper, we establish the Carleman estimates for forward and backward stochastic fourth order Schr\"{o}dinger equations, on basis of which, we can obtain the observability, unique continuation property and the exact controllability for the forward and backward stochastic fourth order Schr\"{o}dinger equations.