The differentiability of the drag with respect to the variations of a Lipschitz domain in a Navier-Stokes flow

SIAM Journal on Control and Optimization

Volumn 35, Issue 2, 1997, Pages 626-640

  Bello, Juan Antonio ^a   Fernández Cara, Enrique ^a   Lemoine, Jérôme ^b   Simon, Jacques ^b  

^a UNIVERSITY OF SEVILLE   (Spain)

^b UNIVERSITÉ BLAISE PASCAL   (France)

Author keywords

Domain optimization; Hydrodynamic drag; Lipschitz domains; Navier Stokes equations; Optimal control

Indexed keywords

CONFORMAL MAPPING; DRAG; FLOW OF FLUIDS; HYDRODYNAMICS; NAVIER STOKES EQUATIONS; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; VARIATIONAL TECHNIQUES;

DOMAIN OPTIMIZATION; ELLIPTIC EQUATIONS; HYDRODYNAMIC DRAG; LIPSCHITZ DOMAINS;

DIFFERENTIATION (CALCULUS);

EID: 0031100298     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012994278213     Document Type: Article

References (17)

1. J.A. BELLO, E. FERNÁNDEZ-CARA, AND J. SIMON, Optimal shape design for Navier-Stokes flow, in System Modelling and Optimization, Lecture Notes in Control and Inform. Sci. 180, P. Kall, ed., Springer-Verlag, Berlin, 1992, pp. 481-489.
2. J.A. BELLO, E. FERNÁNDEZ-CARA, AND J. SIMON, Variation par rapport au domaine de l'énergie visqueuse dissipée dans un fluide de Navier-Stokes, C. R. Acad. Sci. Paris Sér. I Math., 313 (1991), pp. 447-450.
3. n, C. R. Acad. Sci. Paris Sér. A, 277 (1973), pp. 905-907.
4. R. DAUTRAY AND J.L. LIONS, Analyse mathématique et calcul numérique pour les sciences et les techniques, tome 1, Masson, Paris, 1984.
5. D. GILBARG AND N.S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, Berlin, 1983.
6. V. GIRAULT AND P.A. RAVIART Finite Element Methods for Navier-Stokes Equations, Springer-Verlag, Berlin, 1983.
7. O.A. LADYZHENSKAYA, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York, 1969.
8. J. LEMOINE, Couplage et contrôle pour les équations de Navier-Stokes: Espaces fonctionnels, Thesis, Université Blaise Pascal (Clermont-Ferrand 2), 1995.
9. F. MURAT AND J. SIMON, Quelques résultats sur le contrôle par un domaine géométrique, Report of L.A. 189 74003, Université Paris VI, 1974.
10. F. MURAT AND J. SIMON, Sur le contrôle par un domaine géométrique, Report of L.A. 189 76015, Université Paris VI, 1976.
11. J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson, Paris, 1967.
12. O. PIRONNEAU, On optimum design in fluid mechanics, J. Fluid. Mech., 64 (1974), pp. 97-110.
13. O. PIRONNEAU, Optimal Shape Design for Elliptic Systems, Springer-Verlag, New York, 1984.
14. H. SCHLICHTING, Boundary Layer Theory, Academic Press, New York, 1970.
15. J. SIMON, Differentiation with respect to the domain in boundary value problems, Numer. Funct. Anal. Optim., 2 (1980), pp. 649-687.
16. J. SIMON, Second variation in domain optimization problems, in Control and Estimation of Distributed Parameter Systems, Internat. Ser. Numer. Math. 91, F. Kappel, K. Kunisch, and W. Schappacher, eds., Birkhäuser, Basel, 1989, pp. 361-378.
17. J. SIMON, Domain variation for drag in Stokes flow, in Control Theory of Distributed Parameter Systems and Applications, Lecture Notes in Control and Inform. Sci. 159, X. Li and J. Yong, eds., Springer-Verlag, Berlin, 1991, pp. 28-42.