A priori estimates for the Euler equation with a free boundary

被引：1

作者：

Schweizer, B ^{[1
]}

机构：

[1] Univ Heidelberg, Inst Angew Math, D-6900 Heidelberg, Germany

来源：

EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS | 2005年

关键词：

WATER-WAVE PROBLEM; SURFACE-TENSION; WELL-POSEDNESS; SOBOLEV SPACES; MOTION; FLUID;

D O I：

10.1142/9789812702067_0064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a result for an incompressible ideal fluid with a free surface subject to surface tension; it is not assumed that the fluid is irrotational. A priori estimates are shown by combining energy and vorticity estimates. We indicate how these results can be used in order to derive a local existence result with a Navier-Stokes approximation.

引用

页码：401 / 406

页数：6

共 11 条

[1]

Beyer K, 1998, MATH METHOD APPL SCI, V21, P1149, DOI 10.1002/(SICI)1099-1476(199808)21:12<1149::AID-MMA990>3.0.CO

[2]

2-C

[3]

Christodoulou D, 2000, COMMUN PUR APPL MATH, V53, P1536, DOI 10.1002/1097-0312(200012)53:12<1536::AID-CPA2>3.3.CO

[4]

2-H

[5] THE EQUATIONS OF MOTION OF A PERFECT FLUID WITH FREE-BOUNDARY ARE NOT WELL POSED [J].

EBIN, DG .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1987, 12 (10) :1175-1201

[6]

Iguchi T., 1999, Adv. Math. Sci. Appl., V9, P415

[7] Free boundary problem for an incompressible ideal fluid with surface tension [J].

Ogawa, M ;

Tani, A .

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2002, 12 (12) :1725-1740

[8]

SCHWEIZER B, IN PRESS 3 DIMENSION

[9]

Wagner A, 1999, CH CRC RES NOTES, V409, P246

[10] Well-posedness in Sobolev spaces of the full water wave problem in 3-D [J].

Wu, SJ .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 1999, 12 (02) :445-495

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