Small scale dynamics in incompressible fluid flows

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8. 2D Euler norm inflation

Consider the 2D Euler equation with initial velocity

$u_0 \in H^s, s \in (0,1)$ . Prove norm inflation. Note that the

$L^2$ and

$H^1$ norms are conserved. Same question for

$L^p$ norms with

$p\not=2$ .

Cite this as: AimPL: Small scale dynamics in incompressible fluid flows, available at http://aimpl.org/smallscalefluid.