Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On stability and uniqueness of fluid flow through a rigid porous medium

Author: K. A. Pericak-Spector
Journal: Quart. Appl. Math. 42 (1984), 165-178
MSC: Primary 76S05; Secondary 35Q10
DOI: https://doi.org/10.1090/qam/745097
MathSciNet review: 745097
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study a set of equations describing the flow of an incompressible viscous fluid through a rigid porous medium. Existence, uniqueness and stability results are established for the case of a region impregnated with fluid, and uniqueness for an unsaturated region.

References [Enhancements On Off] (What's this?)

  • [1] W.O. Williams, Constitutive equations for flow of an incompressible viscous fluid through a porous medium, Q. Appl. Math. 36 (1978), 255-267
  • [2] W. O. Williams, On the theory of mixtures, Arch. Rational Mech. Anal. 51 (1973), 239–260. MR 0342045, https://doi.org/10.1007/BF00250532
  • [3] R. Sampaio and W. O. Williams, Thermodynamics of diffusing mixtures, J. Mécanique 18 (1979), no. 1, 19–45 (English, with French summary). MR 527554
  • [4] K. A. Pericak-Spector and W. O. Williams, On work and constraints in mixtures, ZAMP (to appear)
  • [5] E. C. Aifantis, On the problem of diffusion in solids, Acta Mech. 37 (1980), no. 3-4, 265–296 (English, with German summary). MR 586062, https://doi.org/10.1007/BF01202949
  • [6] Jace W. Nunziato and Edward K. Walsh, On ideal multiphase mixtures with chemical reactions and diffusion, Arch. Rational Mech. Anal. 73 (1980), no. 4, 285–311. MR 569595, https://doi.org/10.1007/BF00247672
  • [7] D. S. Drumheller, The theoretical treatment of a porous solid using a mixture theory, Int. J. Solids, Struct. 14 (1978), 441-456
  • [8] A. Bedford and D. S. Drumheller, A variational theory of immiscible mixtures, Arch. Rational Mech. Anal. 68 (1978), no. 1, 37–51. MR 497717, https://doi.org/10.1007/BF00276178
  • [9] Douglas E. Kenyon, The theory of an incompressible solid-fluid mixture, Arch. Rational Mech. Anal. 62 (1976), no. 2, 131–147. MR 0413710, https://doi.org/10.1007/BF00248468
  • [10] Morton E. Gurtin and Guilherme M. de La Penha, On the thermodynamics of mixtures, Arch. Rational Mech. Anal. 36 (1970), no. 5, 390–410. I. Mixtures of rigid heat conductors. MR 1553542, https://doi.org/10.1007/BF00282275
  • [11] Marion L. Oliver, On balanced interactions in mixtures, Arch. Rational Mech. Anal. 49 (1972/73), 195–224. MR 0347299, https://doi.org/10.1007/BF00255666
  • [12] Kathleen Anne Pericak-Spector, ON FLOW THROUGH A. POROUS MEDIUM, ProQuest LLC, Ann Arbor, MI, 1980. Thesis (Ph.D.)–Carnegie Mellon University. MR 2631050
  • [13] H. C. Brinkman, A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appl. Sci. Res. A1 (1947), 27-34
  • [14] H. C. Brinkman, On the permeability of media consisting of closely packed porous particles, Appl. Sci. Res. A1 (1947), 81-86
  • [15] H. C. Brinkman, Problems of fluid flow through swarms of particles and through macromolecules in solution, Research 2 (1949), 190-194
  • [16] R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport phenomena, Wiley, New York, 1960
  • [17] A. E. Scheidegger, The physics of flow through porous media, University of Toronto Press, Toronto, 1974
  • [18] Tsuan Wu Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal. 14 (1963), 1–26. MR 0153255, https://doi.org/10.1007/BF00250690
  • [19] G. I. Barenblatt, In P. Zheltov and I. N. Kochina, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. and Mechanics, PMM 24 (1960), 1286-1303 (transl. of Priklad Mat. Mech. 24 (1960), 852-864)
  • [20] P. J. Chen and M. E. Gurtin, On a theory of heat conduction involving two termperatures, Zeit. fur Angewandte Math. 19 (1968), 614-627
  • [21] Dario Graffi, Il teorema di unicità nella dinamica dei fluidi compressibili, J. Rational Mech. Anal. 2 (1953), 99–106 (Italian). MR 0052270
  • [22] Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin-New York, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147
  • [23] James Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959, pp. 125–263. MR 0108116
  • [24] R. Teman, Navier-Stokes equations, North-Holland, New York, 1977

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 76S05, 35Q10

Retrieve articles in all journals with MSC: 76S05, 35Q10

Additional Information

DOI: https://doi.org/10.1090/qam/745097
Article copyright: © Copyright 1984 American Mathematical Society

American Mathematical Society