An existence result for a free boundary shallow water model using a lagrangian scheme
Flori, F. ; Orenga, P. ; Peybernes, M.
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008), p. 725-741 / Harvested from Numdam
@article{AIHPC_2008__25_4_725_0,
     author = {Flori, F. and Orenga, P. and Peybernes, M.},
     title = {An existence result for a free boundary shallow water model using a lagrangian scheme},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {25},
     year = {2008},
     pages = {725-741},
     doi = {10.1016/j.anihpc.2007.05.005},
     mrnumber = {2436791},
     zbl = {1140.76364},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2008__25_4_725_0}
}
Flori, F.; Orenga, P.; Peybernes, M. An existence result for a free boundary shallow water model using a lagrangian scheme. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) pp. 725-741. doi : 10.1016/j.anihpc.2007.05.005. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_4_725_0/

[1] Asensio M.I., Ferragut L., Simon J., Modelling of convective phenomena in forest fire, Rev. R. Acad. Cien. Serie A Mat. 96 (3) (2002) 299-313. | MR 1985737 | Zbl pre02091903

[2] Beale J.T., Large-time regularity of viscous surface waves, Arch. Rational Mech. 84 (1984) 307-352. | MR 721189 | Zbl 0545.76029

[3] Chatelon F.J., Orenga P., Some smoothness and uniqueness results for a shallow water problem, Adv. Differential Equations 3 (1) (1998) 155-176. | MR 1608014 | Zbl 0953.35117

[4] Ciarlet P.G., Elasticité tridimensionnelle, Collection Recherches en Mathématiques Appliquées, Masson, 1986. | MR 819990 | Zbl 0572.73027

[5] Dautray R., Lions J.L., Analyse Mathématique et Calcul Numérique pour les Sciences et les Techniques, Collection C.E.A., Masson, 1984. | Zbl 0642.35001

[6] Desjardins B., Esteban M.J., Grandmont C., Le Tallec P., Weak solutions for a fluid-elastic structure interaction model, Rev. Mat. Comput. 14 (2) (2001) 523-538. | MR 1871311 | Zbl 1007.35055

[7] Donéa J., Huerta A., Sarrate J., Rodriguez-Ferran A., Arbitrary Lagrangian-Eulerian formulation for fluid-multi rigid bodies interaction problems, Comput. Methods Appl. Mech. Engrg. 190 (24-25) (2001) 3171-3188. | Zbl 0985.76055

[8] Flori F., Giudicelli B., Bornes sur la densité pour un problème de Navier-Stokes compressible à frontière variable avec conditions aux limites de Dirichlet, C. R. Acad. Sci. Paris Ser. I 339 (2004) 251-256. | MR 2092008 | Zbl 1053.35116

[9] Flori F., Giudicelli B., Orenga P., An existence result for a compressible fluid pattern coupled to a cylindrical shell, Nonlinear Anal. Real World Appl. 7 (2006) 308-318. | MR 2192764 | Zbl 1092.76055

[10] Flori F., Morelli C., Orenga P., Convergence of a Lagrangian scheme for a compressible Navier-Stokes model defined on a domain depending on time, Nonlinear Anal. TMA 61 (2005) 759-780. | MR 2130064 | Zbl 1072.76050

[11] Flori F., Orenga P., On a nonlinear fluid-structure interaction problem defined on a domain depending on time, Nonlinear Anal. TMA 38 (1999) 549-569. | MR 1709988 | Zbl 0938.35116

[12] Flori F., Orenga P., Fluid-structure interaction: analysis of a 3-d compressible model, Ann. Inst. H. Poincaré Nonlin. Anal. 17 (2000) 753-777. | Numdam | MR 1804654 | Zbl 0974.35086

[13] Lions P.L., Mathematical Topics in Fluid Mechanics, vol. 1, Oxford University Press, 1996. | MR 1422251 | Zbl 0866.76002

[14] Lions P.L., Mathematical Topics in Fluid Mechanics, vol. 2, Oxford University Press, 1998. | MR 1637634 | Zbl 0908.76004

[15] Di Martino B., Orenga P., Peybernes M., Simulation of a spilled oil slick with a shallow water model with free boundary, Math. Models Methods Appl. Sci. 17 (3) (2007) 393-409. | MR 2311924 | Zbl 1128.35080

[16] Orenga P., Un théorème d'existence de solutions d'un problème de shallow water, Arch. Rational Mach. Anal. 130 (1995) 183-204. | MR 1338456 | Zbl 0839.76007

[17] Di Perna R.J., Lions P.L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511-547. | MR 1022305 | Zbl 0696.34049

[18] Solonnikov V.A., The solvability of the problem of the motion of a viscous incompressible fluid that is bounded by a free surface, Izv. Akad. Nauk SSSR Ser. Mat. 41 (6) (1977) 1388-1424. | MR 495629 | Zbl 0384.76019

[19] Solonnikov V.A., Unsteady motion of a finite mass of fluid bounded by a free surface, J. Soviet Math. 40 (1988) 672-686. | MR 869248 | Zbl 0639.76035