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We consider the inviscid limit for the two-dimensional Navier–Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier–Stokes and Euler velocity fields vanishes in $L^2$ with an order proportional to the square root of the viscosity constant $\nu $. Here, we provide an order $ (\nu /|\log \nu | )^{\frac 12\exp (-Ct)}$ bound, which slightly improves upon earlier results by Chemin.

We study the Fokker–Planck equation as the many-particle limit of a stochastic particlesystem on one hand and as a Wasserstein gradient flow on the other. We write thepath-space rate functional, which characterises the large deviations from the expectedtrajectories, in such a way that the free energy appears explicitly. Next we use thisformulation via the contraction principle to prove that the discrete time rate functionalis asymptotically equivalent in the Gamma-convergence sense to the functional derived fromthe Wasserstein gradient discretization scheme.

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A Note on the Vanishing Viscosity Limit in the Yudovich Class

Wasserstein gradient flows from large deviations ofmany-particle limits

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2 results

A Note on the Vanishing Viscosity Limit in the Yudovich Class

Wasserstein gradient flows from large deviations ofmany-particle limits