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

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

2007-08-03

arxiv.org/abs/0708.0520v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

10.1016/j.physd.2008.03.021

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.

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