The Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity. We prove that a solution exists in a bounded domain provided ∥a∥L2(∂Ω) is less than a computable positive constant and is unique if ∥a∥W 1/2,2(∂Ω) + ∥s∥L2(∂Ω) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ∥a∥L2(∂Ω) + ∥a − u0 · n∥L2(∂Ω) is small.

On the Navier problem for the stationary Navier–Stokes equations

TARTAGLIONE, Alfonsina
2011

Abstract

The Navier problem is to find a solution of the steady-state Navier–Stokes equations such that the normal component of the velocity and a linear combination of the tangential components of the velocity and the traction assume prescribed value a and s at the boundary. If Ω is exterior it is required that the velocity converges to an assigned constant vector u0 at infinity. We prove that a solution exists in a bounded domain provided ∥a∥L2(∂Ω) is less than a computable positive constant and is unique if ∥a∥W 1/2,2(∂Ω) + ∥s∥L2(∂Ω) is suitably small. As far as exterior domains are concerned, we show that a solution exists if ∥a∥L2(∂Ω) + ∥a − u0 · n∥L2(∂Ω) is small.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11591/166877
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