6. Exponential growth of the length of Lagrangian flow map for 2D Euler
Find a solution $u$ of 2D Euler with \[\sup_t \|u\|_{C^1(\mathbb{T}^2)} < \infty,\] and a curve, $l$, of finite length such that the length of $\Phi_t(l)$ grows exponentially in time. Here, $\Phi_t$ is the Lagrangian flow map of $u$.Cite this as: AimPL: Small scale dynamics in incompressible fluid flows, available at http://aimpl.org/smallscalefluid.