REGULARITY OF WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS NEAR THE SMOOTH BOUNDARY

被引：0

作者：

Skalak, Zdenek ^{[1
]}

机构：

[1] Czech Tech Univ, Fac Civil Engn, Prague 16629 6, Czech Republic

来源：

ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS | 2005年

关键词：

Navier-Stokes equations; weak solutions; boundary regularity;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Any weak solution u of the Navier-Stokes equations in a bounded domain satisfying the Prodi-Serrin's conditions locally near the smooth boundary cannot have singular points there. This local-up-to-the-boundary boundedness of u in space-time implies the Holder continuity of u up-to-the-boundary in the space variables.

引用

页数：11

共 15 条

[1]

Bergh J., 1976, INTERPOLATION SPACES

[2] Boundary regularity of weak solutions of the Navier-Stokes equations [J].

Choe, HJ .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 149 (02) :211-247

[3]

Galdi GP, 2000, ADV MATH FLUID MECH, P1

[4] ABSTRACT LP ESTIMATES FOR THE CAUCHY-PROBLEM WITH APPLICATIONS TO THE NAVIER-STOKES EQUATIONS IN EXTERIOR DOMAINS [J].

GIGA, Y ;

SOHR, H .

JOURNAL OF FUNCTIONAL ANALYSIS, 1991, 102 (01) :72-94

[5] DOMAINS OF FRACTIONAL-POWERS OF THE STOKES OPERATOR IN L SPACES [J].

GIGA, Y .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1985, 89 (03) :251-265

[6]

Kang K., 2004, PREPRINT, P1

[7]

Neustupa J., 2003, APPL MATH, V48, P547

[8] Local Regularity of Suitable Weak Solutions to the Navier-Stokes Equations Near the Boundary [J].

Seregin, G. A. .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2002, 4 (01) :1-29

[9]

SERRIN J, 1962, ARCH RATION MECH AN, V9, P187

[10] ON THE REGULARITY OF THE PRESSURE OF WEAK SOLUTIONS OF NAVIER-STOKES EQUATIONS [J].

SOHR, H ;

VONWAHL, W .

ARCHIV DER MATHEMATIK, 1986, 46 (05) :428-439

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