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)


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