Abstract
We prove that any weak space-time \(L^2\) vanishing viscosity limit of a sequence of strong solutions of Navier–Stokes equations in a bounded domain of \({\mathbb R}^2\) satisfies the Euler equation if the solutions’ local enstrophies are uniformly bounded. We also prove that \(t-a.e.\) weak \(L^2\) inviscid limits of solutions of 3D Navier–Stokes equations in bounded domains are weak solutions of the Euler equation if they locally satisfy a scaling property of their second-order structure function. The conditions imposed are far away from boundaries, and wild solutions of Euler equations are not a priori excluded in the limit.
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The research of PC is partially funded by NSF Grant DMS-1209394, and the research if VV is partially funded by NSF Grant DMS-1652134.
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Communicated by Edriss S. Titi.
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Constantin, P., Vicol, V. Remarks on High Reynolds Numbers Hydrodynamics and the Inviscid Limit. J Nonlinear Sci 28, 711–724 (2018). https://doi.org/10.1007/s00332-017-9424-z
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DOI: https://doi.org/10.1007/s00332-017-9424-z