Classical solvability of the two-phase Stefan problem in a viscous incompressible fluid flow

被引：13

作者：

Kusaka, Y ^{[1
]}

Tani, A ^{[1
]}

机构：

[1] Keio Univ, Dept Math, Yokohama, Kanagawa 2238522, Japan

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2002年 / 12卷 / 03期

关键词：

incompressible Navier-Stokes equations; Stefan problem; Holder spaces;

D O I：

10.1142/S0218202502001696

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the two-phase Stefan problem for a viscous incompressible fluid which is a model of melting a solid to a liquid or of soldificating a liquid to a solid with a liquid flowing. The unique solvability is established in Holder spaces locally in time. The method of the proof is rather standard, however the result obtained is completely new: the existence in the Holder spaces with the same Holder exponents as the data and the uniqueness also in the same Holder spaces.

引用

页码：365 / 391

页数：27

共 15 条

[1] [Anonymous], 1989, Z ANAL ANWEND
[2] [Anonymous], 1992, SERIES ADV MATH APPL
[3] LOCAL EXISTENCE AND UNIQUENESS OF SOLUTIONS OF THE STEFAN PROBLEM WITH SURFACE-TENSION AND KINETIC UNDERCOOLING
CHEN, XF
REITICH, F
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 164 (02) : 350 - 362
[4] Golovkin K.K., 1968, ZAP NAUCN SEM LENING, V7, P6
[5] CLASSICAL-SOLUTIONS OF THE STEFAN PROBLEM
HANZAWA, EI
[J]. TOHOKU MATHEMATICAL JOURNAL, 1981, 33 (03) : 297 - 335
[6] Ishii M., 1976, INT J MULTIPHAS FLOW, V3, P197, DOI [DOI 10.1016/0301-9322(76)90008-2, 10.1016/0301-9322(76)90008-2]
[7] ITOH S, IN PRESS INITIAL VAL
[8] On the classical solvability of the Stefan problem in a viscous incompressible fluid flow
Kusaka, Y
Tani, A
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 30 (03) : 584 - 602
[9] Ladyzenskaja O. A., 1968, LINEAR QUASILINEAR E, V23
[10] MICHAEL E, 1983, ANNU REV FLUID MECH, V15, P293

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