Observability inequalities on measurable sets for the Stokes system and applications

TL;DR

This paper proves spectral and observability inequalities for the Stokes system on measurable sets, with applications in shape optimization and control theory, advancing understanding of controllability and optimization in fluid dynamics.

Contribution

It introduces new spectral and observability inequalities for the Stokes system on measurable sets, with applications to shape optimization and control problems.

Findings

Spectral inequalities on measurable sets for the Stokes operator

Observability inequalities for non-stationary Stokes system

Applications in shape optimization and time optimal control

Abstract

In this paper, we establish spectral inequalities on measurable sets of positive Lebesgue measure for the Stokes operator, as well as an observability inequalities on space-time measurable sets of positive measure for non-stationary Stokes system. Furthermore, we provide their applications in the theory of shape optimization and time optimal control problems.