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 epsilon-entropy for Holder spaces and for the class of functions that can be obtained by solving the 2D Euler equations with various right-hand sid...

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Bibliographic Details
Published inarXiv.org
Main Author Shirikyan, Armen
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2007
Subjects
Euler-Lagrange equation
Eulers equations
Mathematical analysis
Mathematics - Analysis of PDEs
Mathematics - Optimization and Control
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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 epsilon-entropy for Holder spaces and for the class of functions that can be obtained by solving the 2D Euler equations with various right-hand sides.
ISSN:2331-8422
DOI:10.48550/arxiv.0708.0520