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

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 speci...

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Bibliographic Details
Published in:Communications in mathematical physics 2012-11, Vol.316 (1), p.171-198
Main Authors: Berselli, Luigi Carlo, Spirito, Stefano
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-012-1581-1