On compactness, domain dependence and existence of steady state solutions to compressible isothermal Navier-Stokes equations

Journal of Mathematical Fluid Mechanics

Volumn 7, Issue 4, 2005, Pages 529-573

  Plotnikov, P I ^a   Sokolowski, J ^b  

^a LAVRENTYEV INSTITUTE OF HYDRODYNAMICS   (Russian Federation)

^b UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

Author keywords

Compressible fluids; Drag minimization; Generalized solutions; Navier Stokes equations; Shape optimization

Indexed keywords

COMPRESSIBLE FLOW; DRAG; ISOTHERMS; OPTIMIZATION; PROBLEM SOLVING; SOLUTIONS;

COMPRESSIBLE FLUIDS; DRAG MINIMIZATION; GENERALIZED SOLUTIONS; SHAPE OPTIMIZATION;

NAVIER STOKES EQUATIONS;

COMPRESSIBLE FLUID; DRAG REDUCTION; NAVIER-STOKES EQUATIONS;

EID: 28344452781     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-004-0134-6     Document Type: Article

References (12)

1. E. FEIREISL, Shape optimisation in viscous compressible fluids, Appl. Math. Optim. 47 (2003), 59-78.
2. P. L. LIONS, Mathematical Topics in Fluid Mechanics, Vol. 2, Compressible Models, Clarendon Press, 1998.
3. M. PADULA, Steady Flows of Barotropic Viscous Fluids, in: Classical Problems in Mechanics, R. RUSSO (ed.), Dipartimento di Matematica della Seconda Universita di Napoli, 1997.
4. J. G. HEYWOOD and M. PADULA, On the existence and uniqueness theory for steady compressible viscous flow, in: Fundamental directions in mathematical fluid mechanics, 171-189, Adv. Math. Fluid Mech., Birkhäuser, Basel, 2000.
5. A. NOVOTNY and M. PADULA, Existence and Uniqueness of Stationary solutions for viscous compressible heat conductive fluid with large potential and small non-potential external forces, Siberian Math. Journal 34 (1993), 120-146.
6. P. L. LIONS, The Concentration-Compactness Principle in the Calculus of Variations. The limit case, Part 1, 2, Riv. Mat. Iberoaamericana (1985), 45-121, 145-201.
7. p Theory for the n-dimensional, stationary Navier-Stokes equations and the incompressible limit for compressible fluids. The equilibrium solutions, Comm. Math. Phys. 109 (1987), 229-248.
8. D. GILBARG, and N. S. TRUDINGER, Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983.
9. P. GRISVARD, Elliptic Problems in Nonsmooth Domains, Pitman, 1985.
10. B. KAWOHL, O. PIRONNEAU, L. TARTAR and J. ZOLESIO, Optimal Shape Design, Lecture Notes in Math. 1740, Springer-Verlag, 2000.
11. M. A. KRASNOSELSKY, Positive Solutions to Operator Equations, Fizmatgiz, Moscow, 1962 (in Russian).
12. M. G. CRANDALL and L. TARTAR, Some relations between nonexpansive and order preserving mappings, Proc. AMS 78 (1980), 385-390.