Partial Regularity for Navier-Stokes Equations

被引：0

作者：

Wang, Lihe ^{[1
,2
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Shanghai Jiao Tong Univ, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

JOURNAL OF MATHEMATICAL FLUID MECHANICS | 2025年 / 27卷 / 02期

关键词：

Navier-Stokes equations; Partial regularity; Monotonicity formula; Compactness; SUITABLE WEAK SOLUTIONS; PROOF;

D O I：

10.1007/s00021-025-00929-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Using a more geometric approach, we demonstrate that the solutions to the Navier-Stokes equations remain regular except on a set with a null Hausdorff measure of dimension 1. The proof primarily relies on a new compactness lemma and the monotonicity property of harmonic functions. The combination of linear and nonlinear approximation schemes makes the proof clear and transparent.

引用

页数：13

共 12 条

[1]

[Anonymous], 1969, Quelques mthodes de rsolution des problmes aux limites non linaires

[2] PARTIAL REGULARITY OF SUITABLE WEAK SOLUTIONS OF THE NAVIER-STOKES EQUATIONS [J].

CAFFARELLI, L ;

KOHN, R ;

NIRENBERG, L .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1982, 35 (06) :771-831

[3]

Campanato S., 1966, ANN MAT PUR APPL, V73, P55

[4] On Partial Regularity of Suitable Weak Solutions to the Three-Dimensional Navier-Stokes equations [J].

Ladyzhenskaya, O. A. ;

Seregin, G. A. .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 1999, 1 (04) :356-387

[5] On the movement of a viscous fluid to fill the space [J].

Leray, J .

ACTA MATHEMATICA, 1934, 63 (01) :193-248

[6]

Lin FH, 1998, COMMUN PUR APPL MATH, V51, P241, DOI 10.1002/(SICI)1097-0312(199803)51:3<241::AID-CPA2>3.0.CO

[7]

2-A

[8] THE NAVIER-STOKES EQUATIONS ON A BOUNDED DOMAIN [J].

SCHEFFER, V .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1980, 73 (01) :1-42

[9]

Serrin J., 1963, NONLINEAR PROBLEMS, P1

[10] ON PARTIAL REGULARITY RESULTS FOR THE NAVIER-STOKES EQUATIONS [J].

STRUWE, M .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1988, 41 (04) :437-458

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