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Asymptotic analysis of the Stokes flow with variable viscosity in a thin elastic channel
1. | Laboratory of Mathematics of the University of Saint-Etienne (LaMUSE), University Jean Monnet, 23, rue Dr Paul Michelon 42023 Saint-Etienne |
2. | Institute of Mathematics “Simion Stoilow”, Romanian Academy, P.O. Box 1-764, 014 700 Bucharest |
References:
[1] |
S. Čanić and A. Mikelić, Effective equations describing the flow of a viscous incompressible fluid through a long elastic tube, C. R. Acad. Sci. Paris, Série IIb, 330 (2002), 661-666. |
[2] |
S. Čanić and A. Mikelić, A two-dimensional effective model describing fluid-structure interaction in blood flow: Analysis, simulation and experimental validation, C. R. Acad. Sci. Mécanique, 333 (2005), 867-883. |
[3] |
C. Conca, J. San Martin and M. Tucsnak, Existence of solutions for the equations modeling the motion of a rigid body in a viscous fluid, Comm. Partial Diff. Eqns., 25 (2000), 1019-1042. |
[4] |
B. Desjardins, M. J. Esteban, C. Grandmont and P. le Talec, Weak solutions for a fluid-structure interaction model, Rev. Mat. Comput., 14 (2001), 523-538. |
[5] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Rational Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[6] |
G. P. Galdi, "An Introduction to the Mathematical Theory of Navier-Stokes Equations," Vol. I, Springer-Verlag, New York, 1994. |
[7] |
V. Girault and P. A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[8] |
C. Grandmont and Y. Maday, Existence for an unsteady fluid-structure interaction problem, M2AN Math. Model. Numer. Anal., 34 (2000), 609-636.
doi: 10.1051/m2an:2000159. |
[9] |
B. M. Haines, I. S. Aranson, L. Berlyand and D. A. Karpeev, Effective viscosity of dilute bacterial suspensions: A two dimensional model, Phys. Biol., 5 (2008), 1-9.
doi: 10.1088/1478-3975/5/4/046003. |
[10] |
J-L. Lions, "Quelques Mèthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod, Gauthier-Villars, Paris, 1969. |
[11] |
S. A. Nazarov and B. A. Plamenevskii, "Elliptic Problems in Domains with Piecewise Smooth Boundaries," Walter de Gruyter, Berlin, 1994. |
[12] |
G. P. Panasenko and R. Stavre, Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl., 85 (2006), 558-579.
doi: 10.1016/j.matpur.2005.10.011. |
[13] |
G. P. Panasenko and R. Stavre, Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall, Networks and Heterogeneous Media, 3 (2008), 651-673. |
[14] |
G. P. Panasenko, Y. Sirakov and R. Stavre, Asymptotic and numerical modelling of a flow in a thin channel with visco-elastic wall, Int. J. Multiscale Comput. Engng., 5 (2007), 473-482.
doi: 10.1615/IntJMultCompEng.v5.i6.40. |
[15] |
D. Serre, Chute libre d'un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., 4 (1987), 99-110. |
[16] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, North-Holland, Amsterdam, 1984. |
show all references
References:
[1] |
S. Čanić and A. Mikelić, Effective equations describing the flow of a viscous incompressible fluid through a long elastic tube, C. R. Acad. Sci. Paris, Série IIb, 330 (2002), 661-666. |
[2] |
S. Čanić and A. Mikelić, A two-dimensional effective model describing fluid-structure interaction in blood flow: Analysis, simulation and experimental validation, C. R. Acad. Sci. Mécanique, 333 (2005), 867-883. |
[3] |
C. Conca, J. San Martin and M. Tucsnak, Existence of solutions for the equations modeling the motion of a rigid body in a viscous fluid, Comm. Partial Diff. Eqns., 25 (2000), 1019-1042. |
[4] |
B. Desjardins, M. J. Esteban, C. Grandmont and P. le Talec, Weak solutions for a fluid-structure interaction model, Rev. Mat. Comput., 14 (2001), 523-538. |
[5] |
B. Desjardins and M. J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Rational Mech. Anal., 146 (1999), 59-71.
doi: 10.1007/s002050050136. |
[6] |
G. P. Galdi, "An Introduction to the Mathematical Theory of Navier-Stokes Equations," Vol. I, Springer-Verlag, New York, 1994. |
[7] |
V. Girault and P. A. Raviart, "Finite Element Methods for Navier-Stokes Equations," Springer-Verlag, Berlin, 1986. |
[8] |
C. Grandmont and Y. Maday, Existence for an unsteady fluid-structure interaction problem, M2AN Math. Model. Numer. Anal., 34 (2000), 609-636.
doi: 10.1051/m2an:2000159. |
[9] |
B. M. Haines, I. S. Aranson, L. Berlyand and D. A. Karpeev, Effective viscosity of dilute bacterial suspensions: A two dimensional model, Phys. Biol., 5 (2008), 1-9.
doi: 10.1088/1478-3975/5/4/046003. |
[10] |
J-L. Lions, "Quelques Mèthodes de Résolution des Problèmes aux Limites Non Linéaires," Dunod, Gauthier-Villars, Paris, 1969. |
[11] |
S. A. Nazarov and B. A. Plamenevskii, "Elliptic Problems in Domains with Piecewise Smooth Boundaries," Walter de Gruyter, Berlin, 1994. |
[12] |
G. P. Panasenko and R. Stavre, Asymptotic analysis of a periodic flow in a thin channel with visco-elastic wall, J. Math. Pures Appl., 85 (2006), 558-579.
doi: 10.1016/j.matpur.2005.10.011. |
[13] |
G. P. Panasenko and R. Stavre, Asymptotic analysis of a non-periodic flow in a thin channel with visco-elastic wall, Networks and Heterogeneous Media, 3 (2008), 651-673. |
[14] |
G. P. Panasenko, Y. Sirakov and R. Stavre, Asymptotic and numerical modelling of a flow in a thin channel with visco-elastic wall, Int. J. Multiscale Comput. Engng., 5 (2007), 473-482.
doi: 10.1615/IntJMultCompEng.v5.i6.40. |
[15] |
D. Serre, Chute libre d'un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., 4 (1987), 99-110. |
[16] |
R. Temam, "Navier-Stokes Equations. Theory and Numerical Analysis," 3rd edition, North-Holland, Amsterdam, 1984. |
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