Regularity of Weak Solutions for the Navier-Stokes Equations Via Energy Criteria

被引：2

作者：

Farwig, Reinhard ^{[1
]}

Kozono, Hideo ^{[1
]}

Sohr, Hermann ^{[1
]}

机构：

[1] Tech Univ Darmstadt, Dept Math, D-64283 Darmstadt, Germany

来源：

ADVANCES IN MATHEMATICAL FLUID MECHANICS: DEDICATED TO GIOVANNI PAOLO GALDI ON THE OCCASION OF HIS 60TH BIRTHDAY, INTERNATIONAL CONFERENCE ON MATHEMATICAL FLUID MECHANICS, 2007 | 2010年

关键词：

Navier-Stokes equations; Weak solutions; Regularity criteria; Energy criteria; Holder continuity;

D O I：

10.1007/978-3-642-04068-9_13

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider a weak solution u of the instationary Navier-Stokes system in a bounded domain of R-3 satisfying the strong energy inequality. Extending previous results by Farwig et al., J. Math. Fluid Mech. 11, 1-14 (2008), we prove among other things that u is regular if either the kinetic energy energy 1/2 vertical bar vertical bar u(t)vertical bar vertical bar 2/3 dissipation enery integral(')(0) vertical bar vertical bar del u(tau)vertical bar vertical bar(2)(2) d tau is (left-side) Holder continuous as a function of time t withHolder exponent and with sufficiently small Holder seminorm. The proofs use local regularity results which are based on the theory of very weak solutions and on uniqueness arguments for weak solutions.

引用

页码：215 / +

页数：3

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