The Drag in a Navier-Stokes Flow with Friction-Driven Boundary Conditions

Matthieu Bonnivard (1)

1 EDP - Equations aux Dérivées Partielles

We consider the drag of an obstacle in a Navier-Stokes flow, associated to the friction-driven boundary conditions introduced by Bucur, Feireisl and Necasova [6]. These boundary conditions account for the asymptotic effect of rough boundaries on the solutions to the Navier-Stokes equations. Consequently, they appear as a natural control variable in order to reduce the drag using the effect of micro-rugosities. In this paper, we prove the existence of a drag associated to friction-driven boundary conditions, we give a uniqueness criterion and, in the particular case of Navier's friction law, we prove that the drag is differentiable with respect to the friction coeffcient, and compute its gradient.

Domaines: Equations aux dérivées partielles [math.AP]

Matthieu Bonnivard. The Drag in a Navier-Stokes Flow with Friction-Driven Boundary Conditions. 2011. ⟨hal-00565411⟩