Non null controllability of Stokes equations with memory
ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 72.

In this paper, we consider the null controllability problem for the Stokes equations with a memory term. For any positive final time T > 0, we construct initial conditions such that the null controllability does not hold even if the controls act on the whole boundary. We also prove that this negative result holds for distributed controls.

DOI : 10.1051/cocv/2019067
Classification : 93B05, 93B07, 76D07, 35K10
Mots-clés : Stokes equations with memory, lack of null controllability, observability inequality 
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     author = {Fern\'andez-Cara, Enrique and Machado, Jos\'e Lucas F. and Souza, Diego A.},
     title = {Non null controllability of {Stokes} equations with memory},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {26},
     year = {2020},
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     zbl = {1451.93023},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/cocv/2019067/}
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Fernández-Cara, Enrique; Machado, José Lucas F.; Souza, Diego A. Non null controllability of Stokes equations with memory. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 72. doi : 10.1051/cocv/2019067. http://www.numdam.org/articles/10.1051/cocv/2019067/

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