Solutions faibles pour des problèmes d’interaction fluide-structure
Benoît Desjardins[1]; Maria J. Esteban[2]
- [1] CEA/DIF, B.P. 12, 91680 Bruyères-le-Châtel, France.
- [2] CEREMADE (UMR 7534), Université Paris-Dauphine, Place de Lattre de Tassigny, 75775 Paris Cedex 16, France.
Séminaire Équations aux dérivées partielles (1999-2000)
- Volume: 1999-2000, page 1-10
Access Full Article
topAbstract
topHow to cite
topReferences
top- C. Conca, J. San Martin, M. Tucsnak, Analysis of a fluid-rigid body problem, C. R. Acad. Sci. Paris Sér. I Math. 328 (199 9), no. 6, p. 473–478. Zbl0937.76012MR1680008
- B. Desjardins, On weak solutions of the compressible isentropic Navier-Stokes equations. Applied Math. Letters, Vol 12, (7), (1999), p. 107–111. Zbl0939.35142MR1750068
- B. Desjardins, M.J. Esteban, Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. for Rat. Mech. Anal., (146) (1999) p. 59-71. Zbl0943.35063MR1682663
- B. Desjardins, M.J. Esteban, On weak solutions for fluid-rigid structure interaction : compressible and incompressible models, to appear in Comm. P. D. E. (1999). Zbl0953.35118MR1765138
- B. Desjardins, M.J. Esteban, C. Grandmont, P. Le Tallec, Weak solutions for a fluid-elastic structure interaction model. En préparation. Zbl1007.35055
- R.J. Di Perna, P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math.98 (1989), p. 511-547. Zbl0696.34049MR1022305
- D. Errate, M.J. Esteban, Y. Maday, Couplage fluide-structure. Un modèle simplifié en dimension 1. C. R. Acad. Sci. Paris Sér. I Math.318 (1994), no. 3, p. 275-281. Zbl0796.73048MR1262911
- G.P. Galdi, J.G. Heywood, Y. Shibata, On the global existence and convergence to steady state of Navier-Stokes flow past an obstacle that is started from rest, Arch. Rational Mech. Anal.138 (1997), no. 4, p. 307-318. Zbl0898.35071MR1467557
- C. Grandmont, Y. Maday, Existence de solutions d’un problème de couplage fluide-structure bidimensionnel instationnaire, C. R. Acad. Sci. Paris Sér. I Math.326 (1998), p. 525-530. Zbl0924.76022
- K.-H. Hoffmann, V.N. Starovoitov, On a motion of a solid body in a viscous fluid. Two-dimensional case, Adv. Math. Sci. Appl., 1999, vol.9, N2, p. 633-648. Zbl0966.76016MR1725677
- J. Leray, Essai sur les mouvements plans d’un liquide visqueux que limitent les parois, J. Math. Pures Appl.13 (1934), p. 331-418. Zbl60.0727.01
- P.-L. Lions, Mathematical Topics in Fluid Mechanics, Vol . Incompressible models, and Vol , Compressible Models, Oxford Univ. Press, (1996). Zbl0866.76002MR1422251
- A. Nouri, F. Poupaud, An existence theorem for the multifluid Navier-Stokes problem, J. Differential Equations122 (1995), no. 1, p. 71–88. Zbl0842.35079MR1356130
- A. Quarteroni, M. Tuveri, A. Veneziani, Computational Vascular Fluid Dynamics : Problems, Models and Methods, Report EPFL/DMA 11.98, submitted to Computing and Visualisation in Science, (1998). Zbl1096.76042
- D. Serre, Chute libre d’un solide dans un fluide visqueux incompressible : Existence, Japan J. Appl. Math.4 (1987), no. 1, p. 33-73. Zbl0655.76022
- V.A. Solonnikov, Unsteady motion of a finite mass of fluid, bounded by a free surface, J. Soviet Math.40 (1988), p. 672-686. Zbl0639.76035MR869248
- L. Tartar, The compensated compactness method applied to systems of conservation laws Systems of nonlinear partial differential equations (Oxford, ), p. 263-285, NATO Adv. Sci. Inst. Ser. C : Math. Phys. Sci., , Reidel, Dordrecht-Boston, Mass., . Zbl0536.35003MR725524