Computational visualization of Shnirelman’s compactly supported weak solution

In [A. Shnirelman, On the non-uniqueness of weak solutions of Euler equations, Comm. Pure Appl. Math. L (1997) 1261–1286], Shnirelman described the construction of a weak solution of the 2D incompressible Euler equations on a torus, with compact support in time. In this article, we use computational tools to obtain an explicit approximation of Shnirelman’s flow, with the objective of visualizing its structure. In particular, the construction was based on the use of the 2D inverse energy cascade, and we obtain an illustration on how the inverse cascade is taking place.