Take a look at the wild side

Abstract

The recent results on non-uniqueness of the Euler equations, all based on the theory developed in the papers by Camillo De Lellis and László Székelyhidi Jr., are believed to be connected to the theory of turbulent fluid flow. The solutions presented in these papers are constructed by adding localized, oscillatory plane waves on top of each other. The limit of this construction gives a highly irregular function, and the solutions are therefore called wild solutions. Inspired by the convex integration method given in the papers of De Lellis and Székelyhidi, as well as the Master thesis of Simon Markfelder, we propose an algorithm to construct such wild solutions numerically. We also suggest possible methods to approximately carry out each step in the algorithm, and implement this in a program. Lastly, we present images and movies of the velocity vector field of the generated solutions.