Euler equations are not exactly controllable by a finite-dimensional external force
نویسنده
چکیده
We show that the Euler system is not exactly controllable by a finitedimensional 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 2D Euler equations with various right-hand sides. AMS subject classifications: 35Q35, 93B05, 93C20
منابع مشابه
Controllability of 3D incompressible Euler equations by a finite-dimensional external force
In this paper, we study the control system associated with the incompressible 3D Euler system. We show that the velocity field and pressure of the fluid are exactly controllable in projections by the same finite-dimensional control. Moreover, the velocity is approximately controllable. We also prove that 3D Euler system is not exactly controllable by a finite-dimensional external force.
متن کاملar X iv : 0 70 8 . 05 20 v 1 [ m at h . A P ] 3 A ug 2 00 7 Euler equations are not exactly controllable by a finite - dimensional external force
We show that the Euler system is not exactly controllable by a finitedimensional 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 2D Euler equations with various right-hand sides. AMS subject classifications: 35Q35, 93B05, 93C20
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