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September  2018, 7(3): 447-463. doi: 10.3934/eect.2018022

Null controllability of the incompressible Stokes equations in a 2-D channel using normal boundary control

 1 Indian Institute of Science Education and Research, Kolkata, West Bengal, India 2 Department of Mathematics, Indian Institute of Technology, Bombay, Powai, Mumbai, Maharashtra 400076, India 3 Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-0123, USA

* Corresponding author: Michael Renardy

Received  January 2018 Revised  March 2018 Published  July 2018

Fund Project: Shirshendu Chowdhury acknowledges financial support from an INSPIRE Fellowship. Michael Renardy and Debanjana Mitra acknowledge support from the National Science Foundation under Grant DMS-1514576.

In this paper, we consider the Stokes equations in a two-dimensional channel with periodic conditions in the direction of the channel. We establish null controllability of this system using a boundary control which acts on the normal component of the velocity only. We show null controllability of the system, subject to a constraint of zero average, by proving an observability inequality with the help of a Müntz-Szász Theorem.

Citation: Shirshendu Chowdhury, Debanjana Mitra, Michael Renardy. Null controllability of the incompressible Stokes equations in a 2-D channel using normal boundary control. Evolution Equations & Control Theory, 2018, 7 (3) : 447-463. doi: 10.3934/eect.2018022
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