For forced 2D Euler flows built around Vishik's unstable vortex, the inviscid limit from Navier-Stokes is unique and radial when initial perturbations are o(ν^{a/γ}), but at the critical size ε~ν^{a/γ} there are viscous solutions converging to non-radial non-unique Euler solutions.
Scale invariant bounds for the Kelvin-Helmholtz instability
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abstract
We derive robust long-time a-priori estimates for the Navier-Stokes equation in a two-dimensional infinite strip which are uniform in the Reynolds number. These estimates provide several new scale invariant upper bounds for the size of the mixing layer in the Kelvin-Helmholtz instability.
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Vanishing viscosity non-unique solutions to the forced 2D Euler Equations
For forced 2D Euler flows built around Vishik's unstable vortex, the inviscid limit from Navier-Stokes is unique and radial when initial perturbations are o(ν^{a/γ}), but at the critical size ε~ν^{a/γ} there are viscous solutions converging to non-radial non-unique Euler solutions.