Inviscid Limit of Vorticity Distributions in the Yudovich Class

We prove that given initial data (Formula presented.), forcing (Formula presented.) and any T > 0, the solutions uν of Navier-Stokes converge strongly in (Formula presented.) for any p ∈ [1, ∞) to the unique Yudovich weak solution u of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a by-product of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the Lp vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller-Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids. © 2020 Wiley Periodicals LLC.

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Author Tarek M Elgindi Mathematics