Title: On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions
Abstract: The vanishing viscosity limit is considered for the incompressible 2D Navier-Stokes equations in a bounded domain. Motivated by studies of turbulent flow we suppose Navier's friction condition in the tangential direction, i.e. the creation of a vorticity proportional to the tangential velocity. We prove the existence of the regular solutions for the Navier-Stokes equations with smooth compatible data and of the solutions with bounded vorticity for initial vorticity being only bounded. Finally, we establish a uniform -bound for the vorticity and convergence to the incompressible 2D Euler equations in the inviscid limit.
Publication Year: 1998
Publication Date: 1998-11-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 228
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