Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid. (English. Abridged French version) Zbl 1129.74306
Summary: We study here the two dimensional motion of an elastic body immersed in an incompressible viscous fluid. The body and the fluid are contained in a fixed bounded set \({\Omega}\). We show the existence of a weak solution for regularized elastic deformations as long as elastic deformations are not too important and no collisions occur. A complete proof is given by Boulakia in existence d’une solution faible pour un probléme d’interaction fluide visqueux incompressible-solide élastique (prepublication 104, UVSQ, 2003).
MSC:
| 74F10 | Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) |
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 35Q35 | PDEs in connection with fluid mechanics |
| 74H20 | Existence of solutions of dynamical problems in solid mechanics |
| 76D03 | Existence, uniqueness, and regularity theory for incompressible viscous fluids |
References:
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| [2] | Desjardins, B.; Esteban, M. J.; Grandmont, C.; Le Tallec, P., Weak solutions for a fluid-elastic structure interaction model, Rev. Mat. Complut., 14, 523-538 (2001) · Zbl 1007.35055 |
| [3] | Di Perna, R. J.; Lions, P.-L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., 98, 511-547 (1989) · Zbl 0696.34049 |
| [4] | Lions, P.-L., Mathematical Topics in Fluid Mechanics (1996), Oxford Science Publications · Zbl 0866.76002 |
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