Inverse Cascade Solutions of the Euler Equations

The motion of an ideal incompressible fluid in a two-dimensional domain M is considered. We assume that the initial velocity field is small-scaled, i.e., its Fourier transform is concentrated at high frequences. The extreme case of flows corresponding to solutions of the Euler equations starting from the zero scale is studied. The main result of the paper is that such a solution exists. Its construction uses the variational principle, generalized flows, and continual braids. Bibliography: 5 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 238–244.