Null controllability for stochastic fourth order parabolic equations

TL;DR

This paper proves that linear stochastic fourth order parabolic equations can be driven to zero using control inputs, by establishing a new observability estimate through a novel Carleman estimate and fundamental identity.

Contribution

It introduces a new global Carleman estimate and fundamental identity for stochastic fourth order parabolic operators, enabling null controllability results.

Findings

Established null controllability for stochastic fourth order parabolic equations.

Developed a new Carleman estimate for stochastic fourth order operators.

Derived an observability estimate via duality argument.

Abstract

We establish the null controllability for linear stochastic fourth order parabolic equations. Utilizing the duality argument, the null controllability is reduced to the observability for backward fourth order stochastic parabolic equations, and the desired observability estimate is obtained by a new global Carleman estimate. Our Carleman estimate is based on a new fundamental identity for a stochastic fourth order parabolic operator.