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Steady free fall of one-dimensional bodies in a hyperviscous fluid at low Reynolds number
1. | Dipartimento di Matematica e Fisica "N. Tartaglia", Università Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia |
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
H. Brenner, The Stokes resistance of an arbitrary particle-II: An extension, Chem. Eng. Sci., 19 (1964), 599-629.
doi: 10.1016/0009-2509(64)85051-X. |
[3] |
E. Fried and M. E. Gurtin, Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales, Arch. Ration. Mech. Anal., 182 (2006), 513-554.
doi: 10.1007/s00205-006-0015-7. |
[4] |
G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in Handbook of mathematical fluid dynamics. North-Holland, Amsterdam, 1 (2002), 653-791.
doi: 10.1016/S1874-5792(02)80014-3. |
[5] |
G. G. Giusteri, The multiple nature of concentrated interactions in second-gradient dissipative liquids, Z. Angew. Math. Phys., 64 (2013), 371-380.
doi: 10.1007/s00033-012-0229-5. |
[6] |
G. G. Giusteri and E. Fried, Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, Meccanica, 49 (2014), 2153-2167.
doi: 10.1007/s11012-014-9890-4. |
[7] |
G. G. Giusteri, A. Marzocchi and A. Musesti, Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies, Mech. Res. Commun., 37 (2010), 642-646.
doi: 10.1016/j.mechrescom.2010.09.001. |
[8] |
G. G. Giusteri, A. Marzocchi, and A. Musesti, Nonsimple isotropic incompressible linear fluids surrounding one-dimensional structures, Acta Mech., 217 (2011), 191-204.
doi: 10.1007/s00707-010-0387-5. |
[9] |
G. G. Giusteri, A. Marzocchi, and A. Musesti, Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids, DCDS-B, 19 (2014), 2145-2157.
doi: 10.3934/dcdsb.2014.19.2145. |
[10] |
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media, Martinus Nijhoff Publishers, The Hague, 1983. |
[11] |
A. Musesti, Isotropic linear constitutive relations for nonsimple fluids, Acta Mech., 204 (2009), 81-88.
doi: 10.1007/s00707-008-0050-6. |
[12] |
H. F. Weinberger, Variational properties of steady fall in Stokes flow, J. Fluid Mech., 52 (1972), 321-344.
doi: 10.1017/S0022112072001442. |
show all references
References:
[1] |
S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math., 12 (1959), 623-727.
doi: 10.1002/cpa.3160120405. |
[2] |
H. Brenner, The Stokes resistance of an arbitrary particle-II: An extension, Chem. Eng. Sci., 19 (1964), 599-629.
doi: 10.1016/0009-2509(64)85051-X. |
[3] |
E. Fried and M. E. Gurtin, Tractions, balances, and boundary conditions for nonsimple materials with application to liquid flow at small-length scales, Arch. Ration. Mech. Anal., 182 (2006), 513-554.
doi: 10.1007/s00205-006-0015-7. |
[4] |
G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in Handbook of mathematical fluid dynamics. North-Holland, Amsterdam, 1 (2002), 653-791.
doi: 10.1016/S1874-5792(02)80014-3. |
[5] |
G. G. Giusteri, The multiple nature of concentrated interactions in second-gradient dissipative liquids, Z. Angew. Math. Phys., 64 (2013), 371-380.
doi: 10.1007/s00033-012-0229-5. |
[6] |
G. G. Giusteri and E. Fried, Slender-body theory for viscous flow via dimensional reduction and hyperviscous regularization, Meccanica, 49 (2014), 2153-2167.
doi: 10.1007/s11012-014-9890-4. |
[7] |
G. G. Giusteri, A. Marzocchi and A. Musesti, Three-dimensional nonsimple viscous liquids dragged by one-dimensional immersed bodies, Mech. Res. Commun., 37 (2010), 642-646.
doi: 10.1016/j.mechrescom.2010.09.001. |
[8] |
G. G. Giusteri, A. Marzocchi, and A. Musesti, Nonsimple isotropic incompressible linear fluids surrounding one-dimensional structures, Acta Mech., 217 (2011), 191-204.
doi: 10.1007/s00707-010-0387-5. |
[9] |
G. G. Giusteri, A. Marzocchi, and A. Musesti, Nonlinear free fall of one-dimensional rigid bodies in hyperviscous fluids, DCDS-B, 19 (2014), 2145-2157.
doi: 10.3934/dcdsb.2014.19.2145. |
[10] |
J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media, Martinus Nijhoff Publishers, The Hague, 1983. |
[11] |
A. Musesti, Isotropic linear constitutive relations for nonsimple fluids, Acta Mech., 204 (2009), 81-88.
doi: 10.1007/s00707-008-0050-6. |
[12] |
H. F. Weinberger, Variational properties of steady fall in Stokes flow, J. Fluid Mech., 52 (1972), 321-344.
doi: 10.1017/S0022112072001442. |
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