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

• Published in: Physica. D Vol. 237; no. 10; pp. 1317 - 1323
• Main Author: Shirikyan, Armen
• Format: Journal Article
• Language: English
• 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

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-...