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Weak solutions to stationary equations of heat transfer in a magnetic fluid

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  • We consider the differential system describing the stationary heat transfer in a magnetic fluid in the presence of a heat source and an external magnetic field. The system consists of the stationary incompressible Navier-Stokes equations, the magnetostatic equations and the stationary heat equation. We prove, for the differential system posed in a bounded domain of $\mathbb{R}^3$ and equipped with Fourier boundary conditions, the existence of weak solutions by using a regularization of the Kelvin force and the thermal power.

    Mathematics Subject Classification: Primary: 35Q35, 76D05.

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  •   R. Alexandre  and  C. Villani , On the Boltzmann equation for long-range interactions, Comm. Pure Appl. Math., 55 (2002) , 30-70.  doi: 10.1002/cpa.10012.
      Y. Amirat  and  K. Hamdache , Heat transfer in incompressible magnetic fluid, J. Math. Fluid Mech., 14 (2012) , 217-247.  doi: 10.1007/s00021-011-0050-5.
      Y. Amirat  and  K. Hamdache , Global weak solutions to the equations of thermal convection in micropolar fluids subjected to Hall current, Nonlinear Analysis, Series A: Theory, Methods & Applications, 102 (2014) , 186-207.  doi: 10.1016/j.na.2014.02.001.
      H. I. Andersson  and  O. A. Valnes , Flow of a heated ferrofluid over a stretching sheet in the presence of a magnetic dipole, Acta Mech., 128 (1998) , 39-47. 
      B. Ducomet  and  E. Feireisl , On the dynamics of gaseous stars, Arch. Rational Mech. Anal., 174 (2004) , 221-266.  doi: 10.1007/s00205-004-0326-5.
      E. Feireisl, Dynamics of Viscous Compressible Fluids, Oxford University Press, 2004.
      E. Feireisl and D. Prazak, Asymptotic Behavior of Dynamical Systems in Fluid Mechanics, AIMS Series on Applied Mathematics, 4, Springfield, MO, 2010.
      E. Feireisl  and  J. Málek , On the Navier-Stokes equations with temperature-dependent transport coefficients, Differential Equations and Nonlinear Mechanics, (2006) , 1-14. 
      G. P. Galdi, An Introduction to The Mathematical Theory of The Navier-Stokes Equations. I. Linearized Steady Problems, Springer tracts in Natural Philosophy, 38, Springer Verlag, New-York, 1994. doi: 10.1007/978-1-4612-5364-8.
      G. P. Galdi, An Introduction to The Mathematical Theory of the Navier-Stokes Equations. II. Nonlinear Steady Problems, Springer tracts in Natural Philosophy, 39, Springer Verlag, 1994. doi: 10.1007/978-1-4612-5364-8.
      P. Grisvard, Elliptic Problems in Non Smooth Domains, Pitman, 1985.
      D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York, 1980.
      J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod-Gauthier-Villars, 1969.
      P. B. Mucha  and  M. Pokorny , Weak solutions to equations of steady compressible heat conducting fluids, Mathematical Models and Methods in Applied Sciences, 20 (2010) , 785-813.  doi: 10.1142/S0218202510004441.
      P. B. Mucha  and  M. Pokorny , On the steady compressible Navier-Stokes-Fourier system, Commun. Math. Phys, 288 (2009) , 349-377.  doi: 10.1007/s00220-009-0772-x.
      A. Novotný and I. Straškraba, Introduction to the Mathematical Theory of Compressible Flow, Oxford University Press, 2004.
      Q. Q. A. Pankhurst , J. Connolly , S. K. Jones  and  J. Dobson , Applications of magnetic nonoparticles in biomedicine, J. Phys. D: Appl. Phys., 36 (2003) , 167-181. 
      A. Prignet , Conditions aux limites non homogènes pour des problènmes elliptiques avec second membre mesure, Ann. Fac. Sciences Toulouse, 6 (1997) , 297-318. 
      R. E. Rosensweig, Ferrohydrodynamics, Dover Publications, Inc. 1997.
      R. E. Rosensweig, Basic equations for magnetic fluids with internal rotations, in Ferrofluids: Magnetically Controllable Fluids and Their Applications, Lecture Notes in Physics (SpringerVerlag, Heidelberg), 594, S. Odenbache Ed., (2002), 61-84.
      M. I. Shliomis, in Ferrofluids: Magnetically controllable fluids and their applications, Lecture Notes in Physics (Springer-Verlag, Heidelberg), S. Odenbach Ed., 594 (2002), 85-111.
      R. Temam, Navier-Stokes Equations, 3rd (revised) edition, Elsevier Science Publishers B.V., Amsterdam, 1984.
      E. E. Tzirtzilakis  and  N. G. Kafoussias , Biomagnetic fluid flow over a stretching sheet with nonlinear temperature dependent magnetization, Z. Angew. Math. Phys., 54 (2003) , 551-565.  doi: 10.1007/s00033-003-1100-5.
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