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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
