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On the Vanishing Viscosity Limit of 3D Navier-Stokes Equations under Slip Boundary Conditions in General Domains

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Abstract

We consider the vanishing-viscosity limit for the Navier-Stokes equations with certain slip-without-friction boundary conditions in a bounded domain with non-flat boundary. In particular, we are able to show convergence in strong norms for a solution starting with initial data belonging to the special subclass of data with vanishing vorticity on the boundary. The proof is obtained by smoothing the initial data and by a perturbation argument with quite precise estimates for the equations of the vorticity and for that of the curl of the vorticity.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U. Dini”, Università degli Studi di Pisa, Via F. Buonarroti 1/c, 56127, Pisa, Italy

    Luigi Carlo Berselli

  2. Dipartimento di Matematica, Università dell’Aquila, via Vetoio 1, 67010, Coppito (AQ), Italy

    Stefano Spirito

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  1. Luigi Carlo Berselli
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  2. Stefano Spirito
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Correspondence to Luigi Carlo Berselli.

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Communicated by P. Constantin

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Berselli, L.C., Spirito, S. On the Vanishing Viscosity Limit of 3D Navier-Stokes Equations under Slip Boundary Conditions in General Domains. Commun. Math. Phys. 316, 171–198 (2012). https://doi.org/10.1007/s00220-012-1581-1

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