Small scale dynamics in incompressible fluid flows

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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.