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. © 2012 Springer-Verlag Berlin Heidelberg.

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

SPIRITO, STEFANO
2012

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. © 2012 Springer-Verlag Berlin Heidelberg.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11697/111478
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