Abstract
We construct a Navier-Stokes flow in the unit disk, whose initial data have radially symmetric vorticity. Our goal is to show that this flow is convergent to some Euler flow as the viscosity tends to zero inL 2 norm. For the purpose we give necessary and sufficient conditions for this convergence inC([0,T];L 2 (μ)), where μ is a two dimensional bounded domain with smooth boundary.
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Matsui, S. Example of zero viscosity limit for two dimensional nonstationary Navier-Stokes flows with boundary. Japan J. Indust. Appl. Math. 11, 155–170 (1994). https://doi.org/10.1007/BF03167219
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DOI: https://doi.org/10.1007/BF03167219