Geodesic
On classical solvability of the multidimensional Stefan problem for convective motion of a viscous incompressible fluid
Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 1-17 
B. V. Bazalii; S. P. Degtyarev. On classical solvability of the multidimensional Stefan problem for convective motion of a viscous incompressible fluid. Sbornik. Mathematics, Tome 60 (1988) no. 1, pp. 1-17. http://geodesic.mathdoc.fr/item/SM_1988_60_1_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Stefan problem for a quasilinear parabolic equation is considered. Convective motions in the fluid phase are described by the Navier–Stokes system. The existence of a smooth solution locally in time is proved. Bibliography: 15 titles

[1] Cannon Y. R., Benedetto E. D., Kinghtly G. H., “The steady state Stefan problem with convection”, Arch. Ration. Mech. and Anal., 1980, no. 73, 79–97 | DOI | MR | Zbl

[2] Oleinik O. A., “Ob odnom metode resheniya obschei zadachi Stefana”, DAN SSSR, 135:5 (1960), 1054–1057 | MR

[3] Cannon Y. R., Benedetto E. D., Knightly G. H., “The bidimensional Stefan problem with convection the time dependent case”, Commun. Part. Diff. Equat., 8:14 (1983), 1549–1604 | DOI | MR | Zbl

[4] Caffarelli L. A., “Some aspects of one-phase Stefan problem”, Indiana Univ. Math. I, 27 (1978), 73–77 | DOI | MR | Zbl

[5] Kinderlehrer D., Nirenberg L., “The smoothness of the free boundary in the one phase Stefan problem”, Comm. Pure. Appl. Math., 31 (1978), 257–282 | DOI | MR | Zbl

[6] Meirmanov A. M., “O klassicheskom reshenii mnogomernoi zadachi Stefana dlya kvazilineinykh parabolicheskikh uravnenii”, Matem. sb., 112(154):2(6) (1980), 170–192 | MR | Zbl

[7] Hanzawa E.-I., “Classical solutions of the Stefan problem”, Tohoku Math. Journ., 33 (1981), 297–335 | DOI | MR | Zbl

[8] Solonnikov V. A., “Otsenka resheniya odnoi nachalno-kraevoi zadachi dlya lineinoi nestatsionarnoi sistemy uravnenii Nave–Stoksa”, Zap. nauchn. seminarov LOMI, 59 (1976), 178–254 | MR | Zbl

[9] Solonnikov V. A., “O razreshimosti vtoroi nachalno-kraevoi zadachi dlya lineinoi nestatsionarnoi sistemy uravnenii Nave–Stoksa”, Zap. nauchn. seminarov LOMI, 69 (1977), 200–218 | MR | Zbl

[10] Solonnikov V. A., “Razreshimost zadachi o dvizhenii vyazkoi neszhimaemoi zhidkosti, ogranichennoi svobodnoi poverkhnostyu”, Izv. AN SSSR. Ser. matem., 41:6 (1977), 1388–1424 | MR | Zbl

[11] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967, 736 pp. | MR

[12] Solonnikov V. A., “O differentsialnykh svoistvakh resheniya pervoi kraevoi zadachi dlya nestatsionarnoi sistemy uravnenii Nave–Stoksa”, Tr. MIAN, 73, 1964, 221–291 | MR | Zbl

[13] Beitmen G., Erdein A., Tablitsy integralnykh preobrazovanii, Nauka, M., 1969

[14] Bazalii B. V., “Ustoichivost gladkikh reshenii dvukhfaznoi zadachi Stefana”, DAN SSSR, 262:2 (1982), 265–269 | MR | Zbl

[15] Bazalii B. V., “Issledovanie dvukhfaznoi zadachi Stefana v okrestnosti statsionarnogo resheniya”, DAN USSR. Ser. A, 1983, no. 12, 3–7 | MR | Zbl