1. Nonlinear enhanced dissipation for the 2D Euler equation with horizontal viscosity
Consider the 2D Euler equation with horizontal viscosity on $\mathbb{T}\times [0,1]$: \[\partial_t \omega + u \cdot \nabla \omega = \nu \partial_{xx} \omega,\] \[u=\nabla^\perp\Delta^{-1}\omega.\] How large can \(\nu \int_\Omega |\partial_x \omega|^2\) get as $\nu\to 0$ and $t\rightarrow\infty$?Cite this as: AimPL: Small scale dynamics in incompressible fluid flows, available at http://aimpl.org/smallscalefluid.