Quelques problèmes d’irrégularité dans l’interaction fluide-solide
Gérard-Varet, David1
1 DMA, UMR 8553, Ecole Normale Supérieure, 45 rue d’Ulm, F75230 Paris Cedex 05.
Journées équations aux dérivées partielles (2008), article no. 2, 19 p.
DOI : 10.5802/jedp.46
Gérard-Varet, David 1

1 DMA, UMR 8553, Ecole Normale Supérieure, 45 rue d’Ulm, F75230 Paris Cedex 05. 
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Gérard-Varet, David. Quelques problèmes d’irrégularité dans l’interaction fluide-solide. Journées équations aux dérivées partielles (2008), article  no. 2, 19 p. doi : 10.5802/jedp.46. http://archive.numdam.org/articles/10.5802/jedp.46/

[1] Basson, A.; Gérard-Varet, D. Wall laws for fluid flows at a boundary with random roughness, Comm. Pure Appl. Math., Volume 61 (2008) no. 7, pp. 941-987 | MR | Zbl

[2] Casado-Díaz, J.; Fernández-Cara, E.; Simon, J. Why viscous fluids adhere to rugose walls: a mathematical explanation, J. Differential Equations, Volume 189 (2003) no. 2, pp. 526-537 | MR | Zbl

[3] Davis, R.H.; Zhao, Y.; Galvin, K.; Wilson, H.J. Solid-solid contacts due to surface roughness and their effects on suspension behaviour, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., Volume 361 (2003) no. 1806, pp. 871-894 | MR | Zbl

[4] Desjardins, B.; Esteban, M. J. Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Ration. Mech. Anal., Volume 146 (1999) no. 1, pp. 59-71 | MR | Zbl

[5] Galdi, G.P. An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II, Springer Tracts in Natural Philosophy, 39, Springer-Verlag, New York, 1994 (Nonlinear steady problems) | MR | Zbl

[6] Gérard-Varet, D. The Navier wall law at a boundary with random roughness (2008) (To appear in Comm. Math. Physics) | MR | Zbl

[7] Gérard-Varet, D.; Hillairet, M. Regularity issues in the problem of fluid-structure interaction (2008) (Preprint)

[8] Gérard-Varet, D.; Masmoudi, N. Relevance of the slip condition for fluid flows near an irregular boundary (2008) (Preprint)

[9] Happel, J.; Brenner, H. Low Reynolds number hydrodynamics with special applications to particulate media, Prentice-Hall Inc., Englewood Cliffs, N.J., 1965 | MR

[10] Hillairet, M. Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations, Volume 32 (2007) no. 7-9, pp. 1345-1371 | MR

[11] Ladyženskaja, O. A.; Solonnikov, V. A. Determination of solutions of boundary value problems for stationary Stokes and Navier-Stokes equations having an unbounded Dirichlet integral, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), Volume 96 (1980), p. 117-160, 308 (Boundary value problems of mathematical physics and related questions in the theory of functions, 12) | MR | Zbl

[12] Lefevbre, A. Fluid Particle simulation with FREEFEM++, Esaim Proceedings, Volume 18 (2007), pp. 120-132 | MR

[13] Masmoudi, N.; Saint-Raymond, L. From the Boltzmann equation to the Stokes-Fourier system in a bounded domain, Comm. Pure Appl. Math., Volume 56 (2003) no. 9, pp. 1263-1293 | MR | Zbl

[14] Maury, B. A time-stepping scheme for inelastic collisions. Numerical handling of the nonoverlapping constraint, Numer. Math., Volume 102 (2006) no. 4, pp. 649-679 | MR | Zbl

[15] San Martín, J.A.; Starovoitov, V.; Tucsnak, M. Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, Arch. Ration. Mech. Anal., Volume 161 (2002) no. 2, pp. 113-147 | MR | Zbl

[16] Serre, D. Chute libre d’un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., Volume 4 (1987) no. 1, pp. 99-110 | MR | Zbl

[17] Takahashi, T. Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, Adv. Differential Equations, Volume 8 (2003) no. 12, pp. 1499-1532 | MR | Zbl

[18] Ybert, C.; Barentin, C.; Cottin-Bizonne, C.; Joseph, P.; Bocquet, L. Achieving large slip with superhydrophobic surfaces: scaling laws for generic geometries, Phys. Fluids, Volume 19 (2007), pp. 123601 | Zbl

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