Discrete Schrödinger equation and ill-posedness for the Euler equation (Q501435)

The paper deals with the 2D Euler equation in vorticity formulation on the torus. Under periodic boundary conditions in a family of Banach spaces based on the Fourier coefficients the local well-posedness in different topologies is studied. The authors show that the problem under consideration is ill-posed in any neighborhood of 0 in the working family of Banach spaces introduced by the authors. They study flows which are small perturbations of a certain ``Kolmogorov state'' and show that the linear Schrödinger equation is in some sense embedded in the Euler equation, even for arbitrarily short times.