Unique Continuation and Observability Estimates for 2-D Stokes Equations with the Navier Slip Boundary Condition

TL;DR

This paper establishes unique continuation and observability estimates for 2-D Stokes equations with Navier slip boundary conditions, enabling new control applications in fluid dynamics.

Contribution

It introduces a novel unique continuation estimate and a new strategy for observability from partial time data for Stokes equations with slip boundary conditions.

Findings

Unique continuation estimate proven for 2-D Stokes with slip boundary

Observability estimate derived from partial time data

Applications to control problems demonstrated

Abstract

This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of positive measure in time follows from the aforementioned unique continuation estimate and the new strategy developed in [16]. Several applications of the above-mentioned observability estimate to control problems of the Stokes equations are given.