Conditonal Lipschitz stability for the Inverse Problem of the 2D Navier-Stokes System in a Bounded Domain

TL;DR

This paper establishes conditional Lipschitz stability and local recovery methods for an inverse problem related to the 2D Navier-Stokes system with specific boundary conditions, using energy estimates.

Contribution

It introduces a new stability result and local recovery technique for the inverse problem of the 2D Navier-Stokes system with vorticity constraints.

Findings

Proves conditional Lipschitz stability for the inverse problem.

Develops a local recovery method for velocity and boundary vorticity.

Uses energy methods to analyze the vorticity transport equation.

Abstract

This paper concerns an inverse problem for the initial boundary value problem of the two-dimensional Navier-Stokes system defined in a bounded simply connected domain with slip, vorticity boundary conditions, and a global vorticity invariant constraint. We establish conditional Lipschitz stability and a local recovery for this inverse problem, where the velocity field and space-independent boundary vorticity are locally recovered from the given initial velocity field and the global vorticity invariant. Our analysis is based on well-posedness estimates and energy methods for the vorticity transport equation.