Local null controllability of the N-dimensional Navier-Stokes system with N-1 scalar controls in an arbitrary control domain

TL;DR

This paper proves the local null controllability of the N-dimensional Navier-Stokes equations using N-1 scalar controls without restrictions on the control domain, advancing control theory in fluid dynamics.

Contribution

It establishes local null controllability for the N-dimensional Navier-Stokes system with a vanishing control component, removing domain restrictions.

Findings

Achieved controllability with N-1 controls in arbitrary domains

Extended controllability results to N-dimensional Navier-Stokes systems

No domain restrictions required for control application

Abstract

In this paper we deal with the local null controllability of the N-dimensional Navier-Stokes system with internal controls having one vanishing component. The novelty of this work is that no condition is imposed on the control domain.