Remarks on local controllability for the Boussinesq system with Navier boundary condition

Montoya, Cristhian

doi:10.5802/crmath.29

Cited by 1 publication

(4 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The details can be found in [27,Proposition 3.18] and [4,Proposition 4.3]. See also [29] for a similar result.…”

Section: 3mentioning

confidence: 79%

“…Downloaded 01/30/24 to 150.214.182.233 . Redistribution subject to SIAM license or copyright; see https://epubs.siam.org/terms-privacy First, B \varepsi and \theta 1 can be easily bounded using (29) x (H 0,0…”

Section: Technical Profilesmentioning

confidence: 99%

“…Recently, in [25], this result was extended from Leray weak controlled solutions to the case of smooth controlled solutions. For what concerns the Boussinesq system with Navier-slip boundary conditions, see [23,29] for some local results. In section 2, we will reduce the task to the solution of a distributed controllability problem by applying a classical domain extension technique.…”

mentioning

confidence: 99%

“…However, in the spirit of [10,29] one could try to establish a small-time global null controllability for the internal control system (5) in two dimensions by acting only on the temperature. The intuition behind a result of this kind is the following: the temperature \theta is directly controlled by w; then, \theta acts through the coupling term \theta e 2 to control the component u 2 and then u 2 acts as bilinear control through the term u 2 \partial x2 u 1 to control the component u 1 .…”

mentioning

confidence: 99%

See 3 more Smart Citations

Global Controllability of the Boussinesq System with Navier-Slip-with-Friction and Robin Boundary Conditions

Chaves-Silva

Fernández-Cara

Balc’h

et al. 2023

SIAM J. Control Optim.

View full text Add to dashboard Cite

In this paper, we deal with the global exact controllability to the trajectories of the Boussinesq system posed in 2D or 3D smooth bounded domains. The velocity field of the fluid must satisfy a Navier-slip-with-friction boundary condition, and a Robin boundary condition is imposed to the temperature. We assume that one can act on the velocity and the temperature on a small part of the boundary. For the proof, we first transform the boundary control problem into a distributed control problem. Then, we prove a global approximate controllability result by adapting the strategy of Coron, Marbach, and Sueur [J. Eur. Math. Soc. (JEMS ), 22 (2020), pp. 1625--1673]; this relies on the controllability properties of the inviscid Boussinesq system and the analysis of appropriate asymptotic boundary layer expansions. Finally, we conclude with a local controllability result; as in many other cases, this can be established as a consequence of the null controllability of a linearized system through a fixed-point argument. Our contribution can be viewed as an extension of the results in [J. Eur. Math. Soc. (JEMS ), 22 (2020), pp. 1625--1673, where thermal effects were not considered. Thus, we prove that the ideas behind the controllability properties of the Euler system and the well-prepared dissipation technique can be adapted to the present situation. Furthermore, we cover all the classical boundary conditions for the temperature, that is, those of the Robin, Neumann, and Dirichlet kinds.

show abstract

“…The details can be found in [27,Proposition 3.18] and [4,Proposition 4.3]. See also [29] for a similar result.…”

Section: 3mentioning

confidence: 79%

Section: Technical Profilesmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations