On the bilinear control of the Gross-Pitaevskii equation

Chambrion, Thomas; Thomann, Laurent

doi:10.1016/j.anihpc.2020.01.001

Cited by 5 publications

(5 citation statements)

References 28 publications

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“…We are also able to obtain negative controllability results for the nonlinear Schrödinger equation, and this will be treated in our forthcoming paper [7]. Remark 1.3.…”

Section: 2mentioning

confidence: 85%

A Topological Obstruction to the Controllability of Nonlinear Wave Equations with Bilinear Control Term

Chambrion¹,

Thomann²

2019

SIAM J. Control Optim.

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In this paper we prove that the Ball-Marsden-Slemrod controllability obstruction also holds for nonlinear equations, with L 1 bilinear controls. We first show an abstract result and then we apply it to nonlinear wave equations. The first application to the Sine-Gordon equation directly follows from the abstract result, and the second application concerns the cubic wave/Klein-Gordon equation and needs some additional work. 7 3.1. The Sine-Gordon equation 7 3.2. The wave equation in dimension 3 7 Appendix A. Sobolev spaces 12 A.1. Definition 13 A.2. Sobolev embedding theorem 13 Acknowledgments 13 References 13 2000 Mathematics Subject Classification. 35Q93 ; 35L05.

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“…We are also able to obtain negative controllability results for the nonlinear Schrödinger equation, and this will be treated in our forthcoming paper [7]. Remark 1.3.…”

Section: 2mentioning

confidence: 85%

A Topological Obstruction to the Controllability of Nonlinear Wave Equations with Bilinear Control Term

Chambrion¹,

Thomann²

2019

SIAM J. Control Optim.

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“…However, A V also has empty interior in the relative topology of the sphere, see Turinici [19]. More recently, these results were generalised to include the case p = 1 and to Radon measures by Boussaïd, Caponigro and Chambrion [5,6], and to non-linear equations by Chambrion and Thomann [9,10].…”

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confidence: 86%

A remark on the attainable set of the Schrödinger equation

Lampart¹

2021

EECT

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“…In (Chambrion and Thomann, 2018a, Theorem 1.6) we showed in particular that if K ∈ W 1,∞ (R 3 ), the dynamics (1) is non controllable. Under this assumption, the map…”

Section: Ball-marsden-slemrod Obstructionsmentioning

confidence: 98%

“…As in Chambrion and Thomann (2018a), the Strichartz estimates play a major role in the argument, let us recall them in the three-dimensional case.…”

Section: Strichartz Estimatesmentioning

confidence: 99%