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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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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Abstract 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.
AbstractList 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.
Author Shirikyan, Armen
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Cites_doi 10.1007/s002200050546
10.1051/cocv:2000100
10.1007/BF01474610
10.1007/BF00251588
10.1007/s00220-006-0002-8
10.1090/S0002-9904-1966-11586-0
10.1002/1522-2616(200112)232:1<129::AID-MANA129>3.0.CO;2-T
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Exact controllability
Kolmogorov ε -entropy
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Snippet 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...
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SubjectTerms Exact controllability
Kolmogorov [formula omitted]-entropy
Two-dimensional Euler system
Title Euler equations are not exactly controllable by a finite-dimensional external force
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