caa a22 4500 605515840 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00205-015-0887-5 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0887-5 Control and Stabilization of the Benjamin-Ono Equation in $${L^2({\mathbb{T})}}$$ L 2 ( T ) [Elektronische Daten] [Camille Laurent, Felipe Linares, Lionel Rosier] We study the control and stabilization of the Benjamin-Ono equation in $${L^2(\mathbb{T})}$$ L 2 ( T ) , the lowest regularity where the initial value problem is well-posed. This problem was already initiated in Linares and Rosier (Trans Am Math Soc 367:4595-4626, 2015) where a stronger stabilization term was used (that makes the equation of parabolic type in the control zone). Here we employ a more natural stabilization term related to the L 2-norm. Moreover, by proving a theorem of controllability in L 2, we manage to prove the global controllability in large time. Our analysis relies strongly on the bilinear estimates proved in Molinet and Pilod (Anal PDE 5:365-395, 2012) and some new extension of these estimates established here. Springer-Verlag Berlin Heidelberg, 2015 Laurent Camille Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Boite courrier 187, 75252, Paris Cedex 05, France aut Linares Felipe Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil aut Rosier Lionel Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272, Paris Cedex 06, France aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1531-1575 0003-9527 218:3<1531 2015 218 205 https://doi.org/10.1007/s00205-015-0887-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0887-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Laurent Camille Laboratoire Jacques-Louis Lions, CNRS, Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Boite courrier 187, 75252, Paris Cedex 05, France aut NATIONALLICENCE 700 1- Linares Felipe Instituto de Matematica Pura e Aplicada, Estrada Dona Castorina 110, 22460-320, Rio de Janeiro, Brazil aut NATIONALLICENCE 700 1- Rosier Lionel Centre Automatique et Systèmes, MINES ParisTech, PSL Research University, 60 boulevard Saint-Michel, 75272, Paris Cedex 06, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/3(2015-12-01), 1531-1575 0003-9527 218:3<1531 2015 218 205