Abstract
We say that a solution of the Navier–Stokes equations converges in the vanishing viscosity limit to a solution of the Euler equations if their velocities converge in the energy (L 2) norm uniformly in time as the viscosity ν vanishes. We show that a necessary and sufficient condition for the vanishing viscosity limit to hold in a disk is that the space–time energy density of the solution to the Navier–Stokes equations in a boundary layer of width proportional to ν vanish with ν, and that one need only consider spatial variations whose frequencies in the radial or tangential direction lie in a band centered around 1/ν.
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The author was supported in part by NSF grant DMS-0705586 during the period of this work.
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Kelliher, J.P. On the vanishing viscosity limit in a disk. Math. Ann. 343, 701–726 (2009). https://doi.org/10.1007/s00208-008-0287-3
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DOI: https://doi.org/10.1007/s00208-008-0287-3