Global weak solutions to a ferrofluid flow model

Mathematical Methods in the Applied Sciences

Volumn 31, Issue 2, 2008, Pages 123-151

  Amirat, Youcef ^a   Hamdache, Kamel ^b  

^a UNIVERSITÉ BLAISE PASCAL   (France)

^b CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

Author keywords

Magnetic fluid flow; Magnetization; Navier Stokes equations; Weak solutions

Indexed keywords

BOUNDARY VALUE PROBLEMS; FLOW OF FLUIDS; MAGNETIZATION; PROBLEM SOLVING; TORQUE CONTROL;

MAGNETIC FLUID FLOW; WEAK SOLUTIONS;

MAGNETIC FLUIDS;

EID: 37649020891     PISSN: 01704214     EISSN: 10991476     Source Type: Journal    
DOI: 10.1002/mma.896     Document Type: Article

References (30)

1. Shliomis MI. Effective viscosity of magnetic suspension. Soviet Physics JETP 1972; 44:1291-1294.
2. Shliomis MI. Ferrofluids: Magnetically Controllable Fluids and their Applications. Odenbache S (ed.). Lecture Notes in Physics, vol. 594. Springer: Heidelberg, 2002; 85-111.
3. Zahn M. Magnetic fluid and nanoparticle applications to nanotechnology. Journal of Nanoparticle Research 2001; 3(73):73-78.
4. Pankhurst QQA, Connolly J, Jones SK, Dobson J. Applications of magnetic nanoparticles in biomedicine. Journal of Physics D-Applied Physics 2003; 36:R167-R181.
5. Rosensweig RE. Ferrohydrodynamics. Dover: New York, 1997.
6. Duvaut G, Lions J-L. Inéquations en thermoélasticité et magnétohydrodynamique. Archive for Rational Mechanics and Analysis 1972; 46:241-279.
7. Sermange M, Temam R. Some mathematical questions related to MHD equations. Communications on Pure and Applied Mathematics 1983; XXXVI:635-664.
8. Gerbeau J-F, Le Bris C. A coupled system arising in magnetohydrodynamics. Applied Mathematics Letters 1999; 12(3):53-57.
9. Gerbeau JF, Le Bris C. Existence of solution for a density-dependent magnetohydrodynamic equation. Advances in Differential Equations 1997; 2(3):427-452.
10. Inoue H. Magnetic hydrodynamics equations in moving boundaries. Discrete and Continuous Dynamical Systems, 2005; Supplement:397- 402.
11. Eringen AC. Theory of Micropolar Fluids. Journal of Mathematics and Mechanics 1966; 16(1):1-18.
12. Galdi GP, Rionero S. A note on the existence and uniqueness of solutions of the micropolar fluid equations. International Journal of Engineering Science 1977; 15(2):105-108.
13. Lukaszewicz G. Micropolar Fluids: Theory and Applications. Birkhäuser: Basel, 1999.
14. Ortega-Torres EE, Rojas-Medar MA. Magneto-micropolar fluid motion: global existence of strong solutions. Abstract and Applied Analysis 1999; 4(2): 109-125.
15. Amirat Y, Hamdache K, Murat F. Global weak solutions to the equations of motion for magnetic fluids. Journal of Mathematical Fluid Mechanics, to appear.
16. Rinaldi C, Zahn M. Effects of spin viscosity on ferrofluids flow profiles in alternating and rotating magnetic fields. Physics of Fluids 2002; 14(8):2847-2870.
17. Venkatasubramanian S, Kaloni P. Stability, uniqueness of magnetic fluid motions. Proceedings of the Royal Society of London, Series A, London, 2002; 458:1189-1204.
18. Torrey HC. Bloch equations with diffusion terms. Physical Review 1956; 104:563-565.
19. Gaspari GD. Bloch equation for conduction-electron spin resonance. Physical Review 1966; 131(1):215-219.
20. Galdi GP. An Introduction to the Mathematical Theory of the Navier-Stokes Equations. I. Linearized Steady Problems. Springer Tracts in Natural Philosophy, vol. 38. Springer: New York, 1994.
21. Galdi GP. An Introduction to the Mathematical Theory of the Navier-Stokes equations. II. Nonlinear Steady Problems. Springer Tracts in Natural Philosophy, vol. 39. Springer: New York, 1994.
22. Ladyzhenskaya OA. The Mathematical Theory of Viscous Incompressible Flow (revised 2nd edn). Gordon and Breach: London, 1969.
23. Lions J-L. Quelques Méthodes de Résolution des Problèmes aux Limites Non linéaires. Dunod-Gauthier-Villars: Paris, 1969.
24. Lions PL. Mathematical Topics in Fluid Mechanics. Volume 1. Incompressible Models. Oxford Science Publications: Oxford, 1996.
25. Tartar L. Topics in Nonlinear Analysis, vol. 78.13. Publications Mathématiques d'Orsay: Orsay, 1978.
26. Temam R. Navier-Stokes Equations (3rd (revised) edn). Elsevier: Amsterdam, 1984.
27. Dautray R, Lions J-L. Analyse Mathématique et Calcul Numérique Pour les Sciences et les Techniques. T5, Masson, 1984.
28. p(0, T; B). Annali di Mathematica Pura et Applicata, IV 1987; CXLVI:65-96.
29. Lions J-L, Magenes E. Problèmes aux Limites Non Homogènes et Applications, vol. 1. Dunod: Paris, 1968.
30. Simon J. Nonhomogeneous viscous incompressible fluids: existence of velocity, density, and pressure. SIAM Journal of Mathematical Analyses 1990; 21(5):1093-1117.