## On drag differentiability for Lipschitz domains.(English)Zbl 0860.35093

Casas, Eduardo (ed.), Control of partial differential equations and applications. Proceedings of the IFIP TC7/WG-7.2 international conference, Laredo, Spain, 1994. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 174, 11-22 (1996).
The authors study the behavior of the drag $$T$$ associated to a body travelling at uniform velocity $$\gamma$$ in a viscous incompressible fluid governed by the stationary Navier-Stokes equations. $$T$$ is viewed as a function of the shape of the body, and the analysis of the differentiability of the map $$u\to T (\Omega + u)$$, where $$\Omega$$ is the fluid region and $$u$$ is a field describing the body variations, is carried out. $$\Omega$$ is supposed to be a Lipschitz domain and $$u$$ to be Lipschitz-continuous. The differentiability of the map is obtained when $$\gamma$$ is sufficiently small. Its derivative at zero in the direction $$u$$ is also explicitly computed.
For the entire collection see [Zbl 0834.00041].
Reviewer: F.Rosso (Firenze)

### MSC:

 35Q30 Navier-Stokes equations 35B65 Smoothness and regularity of solutions to PDEs 76D05 Navier-Stokes equations for incompressible viscous fluids