Quelques problèmes d’irrégularité dans l’interaction fluide-solide
Gérard-Varet, David
Journées équations aux dérivées partielles, (2008), p. 1-19 / Harvested from Numdam
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Publié le : 2008-01-01
DOI : https://doi.org/10.5802/jedp.46 
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     author = {G\'erard-Varet, David},
     title = {Quelques probl\`emes d'irr\'egularit\'e dans l'interaction fluide-solide},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     year = {2008},
     pages = {1-19},
     doi = {10.5802/jedp.46},
     language = {en},
     url = {http://dml.mathdoc.fr/item/JEDP_2008____A2_0}
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Gérard-Varet, David. Quelques problèmes d’irrégularité dans l’interaction fluide-solide. Journées équations aux dérivées partielles,  (2008), pp. 1-19. doi : 10.5802/jedp.46. http://gdmltest.u-ga.fr/item/JEDP_2008____A2_0/

[1] Basson, A.; Gérard-Varet, D. Wall laws for fluid flows at a boundary with random roughness, Comm. Pure Appl. Math., Tome 61 (2008) no. 7, pp. 941-987 | MR 2410410 | Zbl 1179.35207

[2] Casado-Díaz, J.; Fernández-Cara, E.; Simon, J. Why viscous fluids adhere to rugose walls: a mathematical explanation, J. Differential Equations, Tome 189 (2003) no. 2, pp. 526-537 | MR 1964478 | Zbl 1061.76014

[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., Tome 361 (2003) no. 1806, pp. 871-894 | MR 1995441 | Zbl 1134.76725

[4] Desjardins, B.; Esteban, M. J. Existence of weak solutions for the motion of rigid bodies in a viscous fluid, Arch. Ration. Mech. Anal., Tome 146 (1999) no. 1, pp. 59-71 | MR 1682663 | Zbl 0943.35063

[5] Galdi, G.P. An introduction to the mathematical theory of the Navier-Stokes equations. Vol. II, Springer-Verlag, New York, Springer Tracts in Natural Philosophy, Tome 39 (1994) (Nonlinear steady problems) | MR 1284206 | Zbl 0949.35005

[6] Gérard-Varet, D. The Navier wall law at a boundary with random roughness (2008) (To appear in Comm. Math. Physics) | MR 2470924 | Zbl 1176.35127

[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 195360

[10] Hillairet, M. Lack of collision between solid bodies in a 2D incompressible viscous flow, Comm. Partial Differential Equations, Tome 32 (2007) no. 7-9, pp. 1345-1371 | MR 2354496 | Zbl pre05204439

[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), Tome 96 (1980), p. 117-160, 308 (Boundary value problems of mathematical physics and related questions in the theory of functions, 12) | MR 579479 | Zbl 0463.35069

[12] Lefevbre, A. Fluid Particle simulation with FREEFEM++, Esaim Proceedings, Tome 18 (2007), pp. 120-132 | MR 2404900 | Zbl pre05213260

[13] Masmoudi, N.; Saint-Raymond, L. From the Boltzmann equation to the Stokes-Fourier system in a bounded domain, Comm. Pure Appl. Math., Tome 56 (2003) no. 9, pp. 1263-1293 | MR 1980855 | Zbl 1024.35031

[14] Maury, B. A time-stepping scheme for inelastic collisions. Numerical handling of the nonoverlapping constraint, Numer. Math., Tome 102 (2006) no. 4, pp. 649-679 | MR 2207284 | Zbl 1091.70002

[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., Tome 161 (2002) no. 2, pp. 113-147 | MR 1870954 | Zbl 1018.76012

[16] Serre, D. Chute libre d’un solide dans un fluide visqueux incompressible. Existence, Japan J. Appl. Math., Tome 4 (1987) no. 1, pp. 99-110 | MR 899206 | Zbl 0655.76022

[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, Tome 8 (2003) no. 12, pp. 1499-1532 | MR 2029294 | Zbl 1101.35356

[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, Tome 19 (2007), pp. 123601 | Zbl 1182.76848