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

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 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.

12 pages

References in corpus (2)

• Controllability of 2D Euler and Navier-Stokes Equations by Forcing 4 Modes
• Extensive Properties of the Complex Ginzburg-Landau Equation

Cited by in corpus (4)

• Approximate controllability of Lagrangian trajectories of the 3D Navier-Stokes system by a finite-dimensional force
• Approximate controllability for Navier--Stokes equations in $3D$ rectangles under Lions boundary conditions
• Global controllability of Boussinesq flows by using only a temperature control
• Approximate controllability for Navier--Stokes equations in {\rm 3D} Cylinders under Lions boundary conditions by an explicit saturating set