Voir la notice de l'article provenant de la source Math-Net.Ru
@article{CMFD_2010_35_a9,
author = {R. V. Shamin},
title = {Surface waves on the water of minimal smoothness},
journal = {Contemporary Mathematics. Fundamental Directions},
pages = {126--140},
publisher = {mathdoc},
volume = {35},
year = {2010},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/CMFD_2010_35_a9/}
}
R. V. Shamin. Surface waves on the water of minimal smoothness. Contemporary Mathematics. Fundamental Directions, Proceedings of the Fifth International Conference on Differential and Functional-Differential Equations (Moscow, August 17–24, 2008). Part 1, Tome 35 (2010), pp. 126-140. http://geodesic.mathdoc.fr/item/CMFD_2010_35_a9/
[1] Dyachenko A. I., Zakharov V. E., Kuznetsov E. A., “Nelineinaya dinamika svobodnoi poverkhnosti idealnoi zhidkosti”, Fizika plazmy, 22:10 (1999), 916–928
[2] Nalimov V. I., “Zadacha Koshi—Puassona”, Dinamika sploshnoi sredy, 18, 1974, 104–210 | MR
[3] Nalimov V. I., “Nestatsionarnye vikhrevye volny”, Sib. mat. zhurn., 37:6 (1996), 1356–1366 | MR | Zbl
[4] Nalimov V. I., Pukhnachev V. V., Neustanovivshiesya dvizheniya idealnoi zhidkosti so svobodnoi granitsei, NGU, Novosibirsk, 1975
[5] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1977 | MR | Zbl
[6] Ovsyannikov L. V., “K obosnovaniyu teorii melkoi vody”, Dinamika sploshnoi sredy, 15, Novosibirsk, 1973, 104–125
[7] Shamin R. V., “Ob odnom chislennom metode v zadache o dvizhenii idealnoi zhidkosti so svobodnoi poverkhnostyu”, Sib. zhurn. vychisl. mat., 9:4 (2006), 325–334
[8] Shamin R. V., “O suschestvovanii gladkikh reshenii uravnenii Dyachenko, opisyvayuschikh neustanovivshiesya techeniya idealnoi zhidkosti so svobodnoi poverkhnostyu”, Dokl. RAN, 406:5 (2006), 614–615 | MR | Zbl
[9] Shamin R. V., “K voprosu ob otsenke vremeni suschestvovaniya reshenii sistemy Koshi–Kovalevskoi s primerami v gidrodinamike so svobodnoi poverkhnostyu”, SMFN, 21, 2007, 133–148 | MR
[10] Shamin R. V., Vychislitelnye eksperimenty v modelirovanii poverkhnostnykh voln v okeane, Nauka, M., 2008 | Zbl
[11] Shamin R. V., “Dinamika idealnoi zhidkosti so svobodnoi poverkhnostyu v konformnykh peremennykh”, SMFN, 28, 2008, 3–144 | MR
[12] Shamin R. V., “Ob otsenke vremeni suschestvovaniya reshenii uravneniya, opisyvayuschego poverkhnostnye volny”, Dokl. RAN, 418:5 (2008), 603–604 | MR | Zbl
[13] Craig W., Sulem C., “Numerical simulation of gravity waves”, J. Comput. Phys., 108 (1993), 73–83 | DOI | MR | Zbl
[14] Craig W., Wayne C. E., “Mathematical aspects of surface water waves”, Round Table “Open Problems” Int. Workshop Math. Hydrod. (Moscow, June 12–17, 2006)
[15] Dyachenko A. I., Kuznetsov E. A., Spector M. D., Zakharov V. E., “Analytical description of the free surface dynamics of an ideal fluid (canonical formalism and conformal mapping)”, Phys. Lett. A, 221 (1996), 73–79 | DOI | MR
[16] Hardy G. H., “Weierstrass's nondifferentiable function”, Trans. Amer. Math. Soc., 17 (1916), 301–325 | DOI | MR | Zbl
[17] Nishida T., “A note on a theorem of Nirenberg”, J. Differential Geom., 12 (1977), 629–633 | MR | Zbl
[18] Wu S., “Well-posedness in Sobolev spaces of the full water wave problem in 2-D”, Invent. Math., 130 (1997), 39–72 | DOI | MR | Zbl
[19] Wu S., “Well-posedness in Sobolev spaces of the full water wave problem in 3-D”, J. Amer. Math. Soc., 12:2 (1999), 445–495 | DOI | MR | Zbl
[20] Zakharov V. E., Dyachenko A. I., Vasilyev O. A., “New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface”, European J. Mech. B Fluids, 21 (2002), 283–291 | DOI | MR | Zbl