Euler equations are not exactly controllable by a finite-dimensional external force

We show that the Euler system is not exactly controllable by a finite-dimensional external force. The proof is based on the comparison of the Kolmogorov ε -entropy for Hölder spaces and for the class of functions that can be obtained by solving the two-dimensional Euler equations with various right-...

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Bibliographic Details
Published inPhysica. D Vol. 237; no. 10; pp. 1317 - 1323
Main Author Shirikyan, Armen
Format Journal Article
LanguageEnglish
Published Elsevier B.V 15.07.2008
Subjects
Exact controllability
Kolmogorov [formula omitted]-entropy
Two-dimensional Euler system
Two-dimensional Euler system
Exact controllability
Kolmogorov ε -entropy
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Summary:We show that the Euler system is not exactly controllable by a finite-dimensional external force. The proof is based on the comparison of the Kolmogorov ε -entropy for Hölder spaces and for the class of functions that can be obtained by solving the two-dimensional Euler equations with various right-hand sides.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2008.03.021