Lack of collision between solid bodies in a 2D incompressible viscous flow

Communications in Partial Differential Equations

Volumn 32, Issue 9, 2007, Pages 1345-1371

  Hillairet, M ^a,b  

^a UNIVERSITÉ DE LYON   (France)

^b UNITÉ DE MATHÉMATIQUES PURES ET APPLIQUÉES   (France)

Author keywords

Fluid solid interactions; Global existence; Lack of collision

Indexed keywords

EID: 34548526166     PISSN: 03605302     EISSN: 15324133     Source Type: Journal    
DOI: 10.1080/03605300601088740     Document Type: Article

References (18)

1. Conca, C., San Martín, J. A., Tucsnak, M. (2000) Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid. Comm. Partial Differential Equations 25(5-6):1019-1042.
2. Desjardins, B., Esteban, M. J. (1999). Existence of weak solutions for the motion of rigid bodies in a viscous fluid. Arch. Ration. Mech. Anal. 146(1):59-71.
3. Feireisl, E. (2001). On the motion of rigid bodies in a viscous fluid. Appl. Math. 47(6):463-484.
4. Feireisl, E. (2003a). On the motion of rigid bodies in a viscous compressible fluid. Arch. Ration. Mech. Anal. 167(4):281-308.
5. Feireisl, E. (2003b). On the motion of rigid bodies in a viscous incompressible fluid. J. Evol. Equ. 3(3):419-441.
6. Grandmont, C., Maday, Y. (1998). Existence de solutions d'un problème de couplage fluide-structure bidimensionnel instationnarie. [Existence of solutions for a two-dimensional unsteady fluid structure interaction problem.] C. R. Acad. Sci. Paris Sér. I Math. 326(4):525-530.
7. Gunzburger, M. D., Lee, H.-C., Seregin, G. A. (2000). Global existence of weak solutions for viscous incompressible flows around a moving rigid body in three dimensions. J. Math. Fluid Mech. 2(3):219-266.
8. Hesla, T. I. (2005). Collisions of Smooth Bodies in Viscous Fluids: A Mathematical Investigation. PhD thesis, University of Minnesota, revised version.
9. Hillairet, M. (2005a). Asymptotic collision between solid particles in a Burgers-Hopf fluid. Asymptotic Analysis 43(4).
10. Hillairet, M. (2005b). Interactive Features in Fluid Mechanics. PhD thesis, Ecole normale supérieure de Lyon.
11. Hoffmann, K.-H., Starovoitov, V. N. (1999). On a motion of a solid body in a viscous fluid. Two-dimensional case. Adv. Math. Sci. Appl. 9(2):633-648.
12. San Martín, J. A., Starovoitov, V., Tucsnak, M. (2002). Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. Arch. Ration. Mech. Anal. 161(2):113-147.
13. Starovoitov, V. N. (2002). Behavior of a rigid body in an incompressible viscous fluid near a boundary. (Trento 2002) Internat. Ser. Numer. Math. 147:313-327.
14. Starovoitov, V. N. (2005). Nonuniqueness of a solution to the problem on motion of a rigid body in a viscous incompressible fluid. J. Math. Sci. 130(4):4893-4898.
15. Takahashi, T. (2003). Existence of strong solutions for the problem of a rigid-fluid system. C. R. Math. Acad. Sci. Paris 336(5):453-458.
16. Takahashi, T., Tucsnak, M. (2004). Global strong solutions for the two-dimensional motion of an infinite cylinder in a viscous fluid. J. Math. Fluid Mech. 6(1):53-77.
17. Temam, R. (1977). Navier-Stokes Equations. North-Holland Pub. Co..
18. Vàzquez, J. L., Zuazua, E. (2006). Lack of collision in a simplified Id model for fluid-solid interaction. Math. Models Methods Appl. Sci. 16(5):623-678.