On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid
Ortega, Jaime ; Rosier, Lionel ; Takahashi, Takéo
Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007), p. 139-165 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{AIHPC_2007__24_1_139_0,
     author = {Ortega, Jaime and Rosier, Lionel and Takahashi, Tak\'eo},
     title = {On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {24},
     year = {2007},
     pages = {139-165},
     doi = {10.1016/j.anihpc.2005.12.004},
     mrnumber = {2286562},
     zbl = {pre05144941},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_1_139_0}
}

Ortega, Jaime; Rosier, Lionel; Takahashi, Takéo. On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 139-165. doi : 10.1016/j.anihpc.2005.12.004. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_1_139_0/

[1] Amrouche C., Girault V., Giroire J., Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces, J. Math. Pures Appl. (9) 76 (1) (1997) 55-81. | MR 1429997 | Zbl 0878.35029

[2] Conca C., San Martín J.H., Tucsnak M., Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations 25 (5-6) (2000) 1019-1042. | Zbl 0954.35135

[3] Coron J.-M., On the controllability of 2-D incompressible perfect fluids, J. Math. Pures Appl. (9) 75 (2) (1996) 155-188. | MR 1380673 | Zbl 0848.76013

[4] Coron J.-M., On the null asymptotic stabilization of the two-dimensional incompressible Euler equations in a simply connected domain, SIAM J. Control Optim. 37 (6) (1999) 1874-1896, (electronic). | MR 1720143 | Zbl 0954.76010

[5] Desjardins B., Esteban M.J., Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Rational Mech. Anal. 146 (1) (1999) 59-71. | MR 1682663 | Zbl 0943.35063

[6] Desjardins B., Esteban M.J., On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, Comm. Partial Differential Equations 25 (7-8) (2000) 1399-1413. | Zbl 0953.35118

[7] Feireisl E., On the motion of rigid bodies in a viscous fluid, Appl. Math. 47 (6) (2002) 463-484. | MR 1948192 | Zbl 1090.35137

[8] Feireisl E., On the motion of rigid bodies in a viscous compressible fluid, Arch. Rational Mech. Anal. 167 (4) (2003) 281-308. | MR 1981859 | Zbl 1090.76061

[9] Galdi G.P., On the steady self-propelled motion of a body in a viscous incompressible fluid, Arch. Rational Mech. Anal. 148 (1) (1999) 53-88. | MR 1715453 | Zbl 0957.76012

[10] Galdi G.P., Silvestre A.L., Strong solutions to the problem of motion of a rigid body in a Navier-Stokes liquid under the action of prescribed forces and torques, in: Nonlinear Problems in Mathematical Physics and Related Topics, I, Int. Math. Ser. (N.Y.), vol. 1, Kluwer/Plenum, New York, 2002, pp. 121-144. | Zbl 1046.35084

[11] G.P. Galdi, A.L. Silvestre, Strong solutions to the Navier-Stokes equations around a rotating obstacle, Arch. Rational Mech. Anal., July 2004, in press. | Zbl 1081.35076

[12] Galdi G.P., Silvestre A.L., Strong solutions to the problem of motion of a rigid body in a Navier-Stokes liquid under the action of prescribed forces and torques, in: Nonlinear Problems in Mathematical Physics and Related Topics, I, Int. Math. Ser. (N.Y.), vol. 1, Kluwer/Plenum, New York, 2002, pp. 121-144. | Zbl 1046.35084

[13] Germain P., Muller P., Introduction à la mécanique des milieux continus, Masson, Paris, 1980. | MR 576236 | Zbl 0465.73001

[14] Glass O., Exact boundary controllability of 3-D Euler equation, ESAIM Control Optim. Calc. Var. 5 (2000) 1-44, (electronic). | Numdam | MR 1745685 | Zbl 0940.93012

[15] Grandmont C., Maday Y., Existence for an unsteady fluid-structure interaction problem, Math. Model. Numer. Anal. (M2AN) 34 (3) (2000) 609-636. | Numdam | Zbl 0969.76017

[16] Gunzburger M.D., Lee H.-C., Seregin G.A., Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions, J. Math. Fluid Mech. 2 (3) (2000) 219-266. | MR 1781915 | Zbl 0970.35096

[17] Hartman P., Ordinary Differential Equations, second ed., Birkhäuser, Boston, MA, 1982. | MR 658490

[18] Hishida T., An existence theorem for the Navier-Stokes flow in the exterior of a rotating obstacle, Arch. Rational Mech. Anal. 150 (1999) 307-348. | Zbl 0949.35106

[19] Hoffmann K.-H., Starovoitov V.N., On a motion of a solid body in a viscous fluid. Two-dimensional case, Adv. Math. Sci. Appl. 9 (2) (1999) 633-648. | MR 1725677 | Zbl 0966.76016

[20] Hoffmann K.-H., Starovoitov V.N., Zur Bewegung einer Kugel in einer zähen Flüssigkeit, Doc. Math. 5 (2000) 15-21, (electronic). | MR 1739269 | Zbl 0936.35125

[21] Judakov N.V., The solvability of the problem of the motion of a rigid body in a viscous incompressible fluid, Dinamika Splošn. Sredy 255 (1974) 249-253, (Vyp. 18 Dinamika Zidkost. so Svobod. Granicami). | MR 464811

[22] Kato T., On classical solutions of the two-dimensional nonstationary Euler equation, Arch. Rational Mech. Anal. 25 (1967) 188-200. | MR 211057 | Zbl 0166.45302

[23] Kikuchi K., Exterior problem for the two-dimensional Euler equation, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 30 (1) (1983) 63-92. | MR 700596 | Zbl 0517.76024

[24] Lions J.-L., Magenes E., Non-Homogeneous Boundary Value Problems and Applications. Vol. I, Grundlehren Math. Wiss., Band 181, Springer-Verlag, New York, 1972, (Translated from the French by P. Kenneth). | MR 350177 | Zbl 0223.35039

[25] Lions P.-L., Mathematical Topics in Fluid Mechanics. Vol. 1, Incompressible Models, Oxford Lecture Ser. Math. Appl., vol. 3, The Clarendon Press, Oxford University Press, New York, 1996, Oxford Sci. Publ. | MR 1422251 | Zbl 0866.76002

[26] Munnier A., Zuazua E., Large time behavior for a simplified N-dimensional model of fluid-solid interaction, Comm. Partial Differential Equations 30 (1-3) (2005) 377-417. | Zbl 1080.35088

[27] Ortega J.H., Rosier L., Takahashi T., Classical solutions for the equations modelling the motion of a ball in a bidimensional incompressible perfect fluid, ESAIM: M2AN 39 (1) (2005) 79-108. | Numdam | MR 2136201 | Zbl 1087.35081

[28] San Martín J.H., Starovoitov V., Tucsnak M., Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Rational Mech. Anal. 161 (2) (2002) 113-147. | MR 1870954 | Zbl 1018.76012

[29] Serre D., Chute libre d'un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math. 4 (1) (1987) 99-110. | MR 899206 | Zbl 0655.76022

[30] Silvestre A.L., On the self-propelled motion of a rigid body in a viscous liquid and on the attainability of steady symmetric self-propelled motions, J. Math. Fluid Mech. 4 (4) (2002) 285-326. | MR 1953783 | Zbl 1022.35041

[31] Simon J., Compact sets in the space L p (0,T;B), Ann. Mat. Pura Appl. (4) 146 (1987) 65-96. | MR 916688 | Zbl 0629.46031

[32] Stein E.M., Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Math. Ser., vol. 43, Princeton University Press, Princeton, NJ, 1993, (With the assistance of Timothy S. Murphy, Monographs in Harmonic Analysis, III). | MR 1232192 | Zbl 0821.42001

[33] Takahashi T., Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, Adv. Differential Equations 8 (12) (2003) 1499-1532. | Zbl 1101.35356

[34] Takahashi T., Tucsnak M., Global strong solutions for the two-dimensional motion of an infinite cylinder in a viscous fluid, J. Math. Fluid Mech. 6 (1) (2004) 53-77. | MR 2027754 | Zbl 1054.35061

[35] Temam R., Problèmes mathématiques en plasticité, Gauthier-Villars, Montrouge, 1983. | MR 711964 | Zbl 0547.73026

[36] Temam R., Navier-Stokes Equations, Theory and Numerical Analysis, third ed., North-Holland Publishing Co., Amsterdam, 1984, (With an appendix by F. Thomasset). | Zbl 0568.35002

[37] Vázquez J.L., Zuazua E., Large time behavior for a simplified 1D model of fluid-solid interaction, Comm. Partial Differential Equations 28 (9-10) (2003) 1705-1738. | Zbl 1071.74017