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 Free Access
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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.
W.O. Williams, Constitutive equations for flow of an incompressible viscous fluid through a porous medium, Q. Appl. Math. 36 (1978), 255–267
- W. O. Williams, On the theory of mixtures, Arch. Rational Mech. Anal. 51 (1973), 239–260. MR 342045, DOI https://doi.org/10.1007/BF00250532
- R. Sampaio and W. O. Williams, Thermodynamics of diffusing mixtures, J. Mécanique 18 (1979), no. 1, 19–45 (English, with French summary). MR 527554
K. A. Pericak-Spector and W. O. Williams, On work and constraints in mixtures, ZAMP (to appear)
- 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, DOI https://doi.org/10.1007/BF01202949
- 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, DOI https://doi.org/10.1007/BF00247672
D. S. Drumheller, The theoretical treatment of a porous solid using a mixture theory, Int. J. Solids, Struct. 14 (1978), 441–456
- A. Bedford and D. S. Drumheller, A variational theory of immiscible mixtures, Arch. Rational Mech. Anal. 68 (1978), no. 1, 37–51. MR 497717, DOI https://doi.org/10.1007/BF00276178
- Douglas E. Kenyon, The theory of an incompressible solid-fluid mixture, Arch. Rational Mech. Anal. 62 (1976), no. 2, 131–147. MR 413710, DOI https://doi.org/10.1007/BF00248468
- 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, DOI https://doi.org/10.1007/BF00282275
- Marion L. Oliver, On balanced interactions in mixtures, Arch. Rational Mech. Anal. 49 (1972/73), 195–224. MR 347299, DOI https://doi.org/10.1007/BF00255666
- Kathleen Anne Pericak-Spector, ON FLOW THROUGH A. POROUS MEDIUM, ProQuest LLC, Ann Arbor, MI, 1980. Thesis (Ph.D.)–Carnegie Mellon University. MR 2631050
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
H. C. Brinkman, On the permeability of media consisting of closely packed porous particles, Appl. Sci. Res. A1 (1947), 81–86
H. C. Brinkman, Problems of fluid flow through swarms of particles and through macromolecules in solution, Research 2 (1949), 190–194
R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport phenomena, Wiley, New York, 1960
A. E. Scheidegger, The physics of flow through porous media, University of Toronto Press, Toronto, 1974
- Tsuan Wu Ting, Certain non-steady flows of second-order fluids, Arch. Rational Mech. Anal. 14 (1963), 1–26. MR 153255, DOI https://doi.org/10.1007/BF00250690
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)
P. J. Chen and M. E. Gurtin, On a theory of heat conduction involving two termperatures, Zeit. fur Angewandte Math. 19 (1968), 614–627
- Dario Graffi, Il teorema di unicità nella dinamica dei fluidi compressibili, J. Rational Mech. Anal. 2 (1953), 99–106 (Italian). MR 52270, DOI https://doi.org/10.1512/iumj.1953.2.52004
- Daniel D. Joseph, Stability of fluid motions. I, Springer-Verlag, Berlin-New York, 1976. Springer Tracts in Natural Philosophy, Vol. 27. MR 0449147
- K. Oswatitsch, Physikalische Grundlagen der Strömungslehre, Handbuch der Physik (herausgegeben von S. Flügge), Bd. 8/1, Strömungsmechanik I (Mitherausgeber C. Truesdell), Springer-Verlag, Berlin-Göttingen-Heidelberg, 1959, pp. 1–124 (German). MR 0108115
R. Teman, Navier-Stokes equations, North-Holland, New York, 1977
W.O. Williams, Constitutive equations for flow of an incompressible viscous fluid through a porous medium, Q. Appl. Math. 36 (1978), 255–267
W. O. Williams, On the theory of mixtures, Arch. Rational Mech. Anal. 51 (1973), 239–260
R. Sampaio and W. O. Williams, Thermodynamics of diffusing mixtures, J. Méchanique 18 (1979), 1945–1979
K. A. Pericak-Spector and W. O. Williams, On work and constraints in mixtures, ZAMP (to appear)
E. C. Aifantis, On the problem of diffusion in solids, Acta Mechanica 37 (1980), 265–296
J. W. Nunziato and E. K. Walsh, On ideal multiphase mixtures with chemical reactions and diffusion, Arch. Rational Mech. Anal. 73 (1980), 285–311
D. S. Drumheller, The theoretical treatment of a porous solid using a mixture theory, Int. J. Solids, Struct. 14 (1978), 441–456
A. Bedford and D. S. Drumheller, A variational theory of immiscible mixtures, Arch. Rational Mech. Anal. 68(1978), 37–51
D. E. Kenyon, The theory of an incompressible solid-fluid mixture, Arch. Rational Mech. Anal. 62 (1976), 131–147
M. E. Gurtin and G. de la Penha, On the thermodynamics of mixtures; I. Mixtures of rigid heat conductors, Arch. Rational Mech. Anal. 36(1970), 390–410
M. L. Oliver, On balanced interactions in mixtures, Arch. Rational Mech. Anal. 49 (1972), 195–224
K. A. Pericak-Spector, On flow through a porous medium, Ph. D. Thesis, Department of Mathematics, Carnegie-Mellon University (1980)
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
H. C. Brinkman, On the permeability of media consisting of closely packed porous particles, Appl. Sci. Res. A1 (1947), 81–86
H. C. Brinkman, Problems of fluid flow through swarms of particles and through macromolecules in solution, Research 2 (1949), 190–194
R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport phenomena, Wiley, New York, 1960
A. E. Scheidegger, The physics of flow through porous media, University of Toronto Press, Toronto, 1974
T. W. Ting, Certain non-steady flows of second order fluids, Arch. Rational Mech. Anal. 14 (1963), 1–26
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)
P. J. Chen and M. E. Gurtin, On a theory of heat conduction involving two termperatures, Zeit. fur Angewandte Math. 19 (1968), 614–627
D. Graffi, Il teorema di unicità nella dinamica dei fluidi compressible, JRMA 2 (1953), 99–106
D. D. Joseph, Stability of fluid motions I, Springer-Verlag, Berlin, 1976
J. Serrin, Mathematical principles of classical fluid mechanics, Handbuch der Physik VIII/1, Springer-Verlag, Berlin, 1959
R. Teman, Navier-Stokes equations, North-Holland, New York, 1977
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Article copyright:
© Copyright 1984
American Mathematical Society
