Approximate Controllability of Boussinesq Channel Flows Only through the Temperature
Abstract
Abstract. We show the global approximate controllability of the Boussinesq system with viscosity and diffusion in a planar periodic channel by using only a temperature control supported in a thin strip. At the walls, a slip boundary condition is imposed on the fluid, and the normal derivative of the temperature is assumed to vanish. This contributes a first global controllability result of such type for the Boussinesq system in the presence of physical boundaries. For the proof, we resort to a small-time scaling argument to control the vorticity through a large initial temperature. Moreover, J.-M. Coron’s return method is employed in order to steer the temperature without significantly impacting the vorticity.
Fields of Study & Subjects
Navier-Stokes equation solutions
Fluid Dynamics and Turbulent Flows
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- SIAM Journal on Control and Optimization
- Volume
- 64
- Issue
- 1
- Pages
- 59–75
- Publication date
- 7 January 2026
- Language
- EN