Local exact controllability for the 2 and 3-d compressible Navier-Stokes equations

TL;DR

This paper establishes local exact controllability for 2D and 3D compressible Navier-Stokes equations with boundary controls, using Carleman estimates and observability of linearized adjoint systems.

Contribution

It provides a new controllability result for compressible Navier-Stokes equations on a boundary, employing novel Carleman estimates in negative Sobolev spaces.

Findings

Controllability achieved for 2D and 3D cases

Use of Carleman estimates in negative Sobolev spaces

Analysis of a linearized adjoint system for controllability

Abstract

The goal of this article is to present a local exact controllability result for the 2 and 3-dimensional compressible Navier-Stokes equations on a constant target trajectory when the controls act on the whole boundary. Our study is then based on the observability of the adjoint system of some linearized version of the system, which is analyzed thanks to a subsystem for which the coupling terms are somewhat weaker. In this step, we strongly use Carleman estimates in negative Sobolev spaces.