Controllability properties for the Navier–Stokes system are closely related to observability properties for the adjoint Oseen–Stokes system; boundary observability inequalities are derived, for that adjoint system, that will be appropriate to deal with suitable constrained controls, like finite-dimensional controls supported in a given subset of the boundary. As an illustration, new boundary controllability results for the Oseen–Stokes system are derived. Finally, some further plausible consequences of the derived inequalities, concerning the Navier–Stokes system, are discussed.
DOI: 10.1051/cocv/2014045
Keywords: Oseen–Stokes system, boundary observability inequalities, boundary control
@article{COCV_2015__21_3_723_0, author = {Rodrigues, S\'ergio S.}, title = {Boundary observability inequalities for the {3D} {Oseen{\textendash}Stokes} system and applications}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {723--756}, publisher = {EDP-Sciences}, volume = {21}, number = {3}, year = {2015}, doi = {10.1051/cocv/2014045}, zbl = {1334.35252}, mrnumber = {3358628}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2014045/} }
TY - JOUR AU - Rodrigues, Sérgio S. TI - Boundary observability inequalities for the 3D Oseen–Stokes system and applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2015 SP - 723 EP - 756 VL - 21 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2014045/ DO - 10.1051/cocv/2014045 LA - en ID - COCV_2015__21_3_723_0 ER -
%0 Journal Article %A Rodrigues, Sérgio S. %T Boundary observability inequalities for the 3D Oseen–Stokes system and applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2015 %P 723-756 %V 21 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2014045/ %R 10.1051/cocv/2014045 %G en %F COCV_2015__21_3_723_0
Rodrigues, Sérgio S. Boundary observability inequalities for the 3D Oseen–Stokes system and applications. ESAIM: Control, Optimisation and Calculus of Variations, Volume 21 (2015) no. 3, pp. 723-756. doi : 10.1051/cocv/2014045. http://archive.numdam.org/articles/10.1051/cocv/2014045/
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