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:
[1] | Bello, J. A., \(L^r\) regularity for the Stokes and Navier-Stokes problems, Ann. Math. Pura Appl., 170, 187-206 (1996) · Zbl 0873.35060 |
[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 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.