Equivalence of two inverse boundary value problems for the Navier-Stokes equations

TL;DR

This paper proves that two inverse boundary value problems for the Navier-Stokes equations are equivalent, showing a unique correspondence between boundary data and internal parameters, thus unifying previous approaches.

Contribution

It establishes the equivalence of two inverse boundary value problems for Navier-Stokes equations, clarifying their relationship and simplifying the inverse problem framework.

Findings

Two inverse boundary value problems are shown to be equivalent.

Unique correspondence between boundary data and internal parameters.

Unification of previous inverse problem approaches.

Abstract

In this note, we prove that for the Navier-Stokes equations, a pair of Dirichlet and Neumann data and pressure uniquely correspond to a pair of Dirichlet data and surface stress on the boundary. Hence the two inverse boundary value problems in [2] and [3] are the same.