Spatial decay estimates for plane flow in Brinkman-Forchheimer model
Authors:
Y. Qin and P. N. Kaloni
Journal:
Quart. Appl. Math. 56 (1998), 71-87
MSC:
Primary 35Q35; Secondary 35B45, 76S05
DOI:
https://doi.org/10.1090/qam/1604880
MathSciNet review:
MR1604880
Full-text PDF Free Access
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Additional Information
- K. A. Ames, L. E. Payne, and P. W. Schaefer, Spatial decay estimates in time-dependent Stokes flow, SIAM J. Math. Anal. 24 (1993), no. 6, 1395–1413. MR 1241151, DOI https://doi.org/10.1137/0524081
- K. A. Ames and L. E. Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal. 20 (1989), no. 4, 789–815. MR 1000723, DOI https://doi.org/10.1137/0520056
- Bruno A. Boley, Some observations on Saint-Venant’s principle, Proceedings of the Third U.S. National Congress of Applied Mechanics, Brown University, Providence, R.I., June 11-14, 1958, American Society of Mechanical Engineers, New York, 1958, pp. 259–264. MR 0100395
- Bruno A. Boley, Upper bounds and Saint-Venant’s principle in transient heat conduction, Quart. Appl. Math. 18 (1960/61), 205–207. MR 112591, DOI https://doi.org/10.1090/S0033-569X-1960-0112591-8
R. C. Gilver and S. A. Altobelli, A determination of effective viscosity for the Brinkman-Forchhiemer flow model, J. Fluid Mech. 258, 355–370 (1994)
- Cornelius O. Horgan, Recent developments concerning Saint-Venant’s principle: an update, AMR 42 (1989), no. 11, 295–303. MR 1021553, DOI https://doi.org/10.1115/1.3152414
- C. O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flows, Quart. Appl. Math. 47 (1989), no. 1, 147–157. MR 987903, DOI https://doi.org/10.1090/S0033-569X-1989-0987903-7
- Cornelius O. Horgan and James K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. in Appl. Mech. 23 (1983), 179–269. MR 889288
- C. O. Horgan, Plane entry flows and energy estimates for the Navier-Stokes equations, Arch. Rational Mech. Anal. 68 (1978), no. 4, 359–381. MR 521600, DOI https://doi.org/10.1007/BF00250987
- C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42 (1984), no. 1, 119–127. MR 736512, DOI https://doi.org/10.1090/S0033-569X-1984-0736512-8
- C. O. Horgan and L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math. 35 (1978), no. 1, 97–116. MR 502782, DOI https://doi.org/10.1137/0135008
C. T. Hsu and P. Cheng, Thermal dispersion in a porus medium, Internat. J. Heat Mass Transfer 33, 1587–1597 (1990)
- James K. Knowles, On Saint-Venant’s principle in the two-dimensional linear theory of elasticity, Arch. Rational Mech. Anal. 21 (1966), 1–22. MR 187480, DOI https://doi.org/10.1007/BF00253046
- James K. Knowles, On the spatial decay of solutions of the heat equation, Z. Angew. Math. Phys. 22 (1971), 1050–1056 (English, with German summary). MR 298255, DOI https://doi.org/10.1007/BF01590873
- James K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatics, Indian J. Pure Appl. Math. 14 (1983), no. 7, 791–805. MR 714832
C. Lin, Spatial decay estimates and energy bounds for the Stokes flow equation, SAACM 2, 249–264 (1992)
O. A. Oleinik and G. A. Yosfian, The Saint-Venant’s principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains, Sibirsk. Math. Zh. 19, 1154–1165 (1978); English transl. in Siberian Math. J. 19, 813–822 (1978)
- L. E. Payne, Uniqueness criteria for steady state solutions of the Navier-Stokes equations, Simpos. Internaz. Appl. Anal. Fis. Mat. (Cagliari-Sassari, 1964) Edizioni Cremonese, Rome, 1965, pp. 130–153. MR 0208144
- L. E. Payne and P. W. Schaefer, Some Phragmén-Lindelöf type results for the biharmonic equation, Z. Angew. Math. Phys. 45 (1994), no. 3, 414–432 (English, with English and German summaries). MR 1278684, DOI https://doi.org/10.1007/BF00945929
- J. Chadam and Y. Qin, Spatial decay estimates for flow in a porous medium, SIAM J. Math. Anal. 28 (1997), no. 4, 808–830. MR 1453307, DOI https://doi.org/10.1137/S0036141095290562
K. A. Ames, L. E. Payne, and P. W. Schaefer, Spatial decay estimates in time-dependent Stokes flow, SIAM J. Math. Anal. 24, 1395–1413 (1993)
K. A. Ames and L. E. Payne, Decay estimates in steady pipe flow, SIAM J. Math. Anal. 20, 789–815 (1989)
B. A. Boley, Some observations on Saint-Venant’s principle, Proc. 3rd U.S. Nat. Cong. Appl. Mech., Brown University, Providence, RI, June 11–14, 1958, American Society of Mechanical Engineers, New York, 1958, pp. 259–264
B. A. Boley, Upper bounds and Saint-Venant’s principle in transient heat conduction, Quart. Appl. Math. 18, 205–207 (1960)
R. C. Gilver and S. A. Altobelli, A determination of effective viscosity for the Brinkman-Forchhiemer flow model, J. Fluid Mech. 258, 355–370 (1994)
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: An update, Appl. Mech. Rev. 42, 295–303 (1989)
C. O. Horgan, Decay estimates for the biharmonic equation with applications to Saint-Venant principles in plane elasticity and Stokes flow, Quart. Appl. Math. 42, 147–157 (1989)
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, Adv. Appl. Mech. 23, 179–269 (1983)
C. O. Horgan, Plane entry flows and energy estimates for the Navier-Stokes equations, Arch. Rational Mech. Anal. 68, 359–381 (1978)
C. O. Horgan, L. E. Payne, and L. T. Wheeler, Spatial decay estimates in transient heat conduction, Quart. Appl. Math. 42, 119–127 (1984)
C. O. Horgan and L. T. Wheeler, Spatial decay estimates for the Navier-Stokes equations with application to the problem of entry flow, SIAM J. Appl. Math. 35, 97–116 (1978)
C. T. Hsu and P. Cheng, Thermal dispersion in a porus medium, Internat. J. Heat Mass Transfer 33, 1587–1597 (1990)
J. K. Knowles, On Saint-Venant’s principle in the two dimensional linear theory of elasticity, Arch. Rational Mech. Anal. 21, 1–22 (1966)
J. K. Knowles, On the spatial decay of solutions of the heat equation, J. Appl. Math. Phys. (ZAMP) 22, 1050–1056 (1971)
J. K. Knowles, An energy estimate for the biharmonic equation and its application to Saint-Venant’s principle in plane elastostatics, Indian J. Pure Appl. Math. 14, 791–805 (1983)
C. Lin, Spatial decay estimates and energy bounds for the Stokes flow equation, SAACM 2, 249–264 (1992)
O. A. Oleinik and G. A. Yosfian, The Saint-Venant’s principle in the two-dimensional theory of elasticity and boundary problems for a biharmonic equation in unbounded domains, Sibirsk. Math. Zh. 19, 1154–1165 (1978); English transl. in Siberian Math. J. 19, 813–822 (1978)
L. E. Payne, Uniqueness criteria for steady state solutions of the Navier-Stokes equations, Simpos. Internaz. Appl. Anal. Fis. Math. (Cagliari-Sassari, 1964) Edizioni Cremonese, Rome, 1965, pp. 130–153
L. E. Payne and P. W. Schaefer, Some Phragmén-Lindelof type results for the biharmonic equation, Z. Angew. Math. Phys. (ZAMP) 45, 415–432 (1994)
Y. Qin and J. Chadam, Spatial decay for flow in a porous medium, preprint
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© Copyright 1998
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