| 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: mrenardy@math.vt.edu
Received:
17
November
2017
Accepted:
24
November
2018
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
© EDP Sciences, SMAI 2019
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