Lack of collision in a simplified ID model for fluid-solid interaction

Mathematical Models and Methods in Applied Sciences

Volumn 16, Issue 5, 2006, Pages 637-678

  Vázquez, Juan Luis ^a   Zuazua, Enrique ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Fluid solid interaction; Global existence; Lack of collision

Indexed keywords

EID: 33646519016     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202506001303     Document Type: Article

References (17)

1. M. Boulakia, Existence of weak solutions for the motion of an elastic structure in an incompressible viscous fluid, C. R. Math. Acad. Sci. Paris 336 (2003) 985-990.
2. G. Conca, J. San Martín and M. Tucsnak, Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. Commun. Partial Diff. Eqns. 25 (2000) 1019-1042.
3. B. Desjardins and M. J. Este ban, On weak solutions for fluid-rigid structure interaction: Compressible and incompressible models, Commun. Partial Diff. Eqns. 25 (2000) 1399-1413.
4. A. Doubova and E. Fernández-Cara, Some control results for simplified one-dimensional models of fluid-solid interaction. Math. Models Meth. Appl. Sci. 15 (2005) 783-824.
5. E. Feireisl, On the motion of rigid bodies in a viscous compressible fluid, Arch. Rational Mech. Anal. 167 (2003) 281-308.
6. C. Grandmont and Y. Maday, Existence de solutions d'un problème de couplage fluide-structure bidimensionnel instationnarie, C. R. Acad. Sci. Paris Sér. I Math. 326 (1998) 525-530.
7. O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Ural'tseva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs, Vol. 23 (Amer. Math. Soc., 1968).
8. A. Munnier and E. Zuazua, Large time behavior for a simplified N-dimensional model for fluid-solid interaction, Commun. Partial Diff. Eqns. 30 (2005) 377-417.
9. J. San Martín, V. N. Starovoitov and M. Tucsnak, Global weak solutions for the two dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Rat. Mech. Anal. 161 (2000) 113-147.
10. V. N. Starovoitov, Behavior of a rigid body in an incompressible viscous fluid near a boundary, in Free Boundary Problems (Trento, 2002), Internat. Ser. Numer. Math., Vol. 147 (Birkhäuser, 2004), pp. 313-327.
11. T. Takahashi, Existence of strong solutions for the problem of a rigid-fluid system, C. R. Acad. Sci. Paris. Ser. I 336 (2003) 453-458.
12. T. Takahashi, Analysis of strong solutions for the equations modelling the motion of a rigid-fluid system in a bounded domain, Adv. Diff. Eqns. 8 (2003) 1499-1532.
13. T. Takahashi and M. Tucsnack, Global solutions for the two-dimensional motion of an infinite cylinder in a viscous fluid, J. Math. Fluid Mech. 6 (2004) 53-77.
14. J. L. Vázquez and E. Zuazua, Large time behavior for a simplified 1-D model of fluid-solid interaction. Commun. Partial Diff. Eqns. 28 (2003) 1705-1738.
15. L. Véron, Coercivité et propriétés régularisantes des semi-groupes non-linéaires dans les espaces de Banach, Ann. Fac. Sci. Toulouse 1 (1979) 171-200.
16. n/p,p C. R. Acad. Sci. Paris 335 (2002) 17-22.
17. E. Zuazua, Weakly nonlinear large time behavior in scalar convection-diffusion equations, Diff. Integral Eqns. 6 (1993) 1481-1491.