| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 60 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2018067 | |
| Published online | 25 October 2019 | |
Lack of null controllability of viscoelastic flows*
1
Institut de Mathématiques, Université de Bordeaux, Bordeaux INP, CNRS,
33400
Talence,
France.
2
Department of Mathematics, Indian Institute of Technology Bombay,
Powai,
Mumbai
400076,
Maharashtra,
India.
3
Department of Mathematics, Virginia Tech,
Blacksburg,
VA
24061-0123,
USA.
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
17
November
2017
Accepted:
24
November
2018
Abstract
We consider controllability of linear viscoelastic flow with a localized control in the momentum equation. We show that, for Jeffreys fluids or for Maxwell fluids with more than one relaxation mode, exact null controllability does not hold. This contrasts with known results on approximate controllability.
Mathematics Subject Classification: 35Q35 / 76A10 / 93B05
Key words: Linear viscoelasticity / controllability / microlocal analysis
Michael Renardy and Debanjana Mitra acknowledge support from the National Science Foundation under Grant DMS-1514576. Debayan Maity acknowledges the support of the Agence Nationale de la Recherche Deutsche Forschungsgemeinschaft (ANR-DFG), project INFIDHEM, ID ANR-16-CE92-0028.
© EDP Sciences, SMAI 2019
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.