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) no. 1, pp. 139-165.
@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},
     pages = {139--165},
     publisher = {Elsevier},
     volume = {24},
     number = {1},
     year = {2007},
     doi = {10.1016/j.anihpc.2005.12.004},
     mrnumber = {2286562},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2005.12.004/}
}
TY  - JOUR
AU  - Ortega, Jaime
AU  - Rosier, Lionel
AU  - Takahashi, Takéo
TI  - On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 139
EP  - 165
VL  - 24
IS  - 1
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2005.12.004/
DO  - 10.1016/j.anihpc.2005.12.004
LA  - en
ID  - AIHPC_2007__24_1_139_0
ER  - 
%0 Journal Article
%A Ortega, Jaime
%A Rosier, Lionel
%A Takahashi, Takéo
%T On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 139-165
%V 24
%N 1
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2005.12.004/
%R 10.1016/j.anihpc.2005.12.004
%G en
%F 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) no. 1, pp. 139-165. doi : 10.1016/j.anihpc.2005.12.004. http://www.numdam.org/articles/10.1016/j.anihpc.2005.12.004/

[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 | Zbl

[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

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

[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 | Zbl

[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 | Zbl

[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

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

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

[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 | Zbl

[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

[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

[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

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

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

[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

[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 | Zbl

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

[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

[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 | Zbl

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

[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

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

[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 | Zbl

[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 | Zbl

[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 | Zbl

[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

[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 | Zbl

[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 | Zbl

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

[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 | Zbl

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

[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 | Zbl

[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

[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 | Zbl

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

[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

[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

Cité par Sources :